402. Орлов А.И. Современная прикладная статистика. - Журнал «Заводская лаборатория». 1998. Т.64. No.3. С. 52-60.

MODERN APPLIED STATISTICIAN

А.И.ОРЛОВ1,2

The critical analysis of state -of-the-art applied 	 Statistician is given. The tendencies of development of statistical methods are considered.

1. What the applied statistician to a national economy gives?
So article [1] was named, in which the numerous examples of successful use of methods of an applied mathematical statistician were resulted. At the solution of practical problems. The list of examples can be continued practically is boundless. From activities 1997 it is enough to refer to the generalizing article В.Г.Горского [2], on a thesis А.Н.Гуды [3]. Under the data of Institute of the information Гарфилда (USA) each from the establishing books В.В.Налимова [4,5] was quoted not less than 1000 times (see also monography [6, с.270,274,373]). In any number of the log-book " the Factory laboratory " is activities, in which those or other methods of an applied statistician are applied to the solution of applied problems. Not of time were published in our log-book and generalizing articles [7-9]. 
Therefore undoubtedly is perfect, that the methods of an applied statistician successfully are applied in various branches of a national economy, practically in all areas of a science. According to the report [10, с.157-158] in 1988 the costs in USSR on a statistical analysis of the data were evaluated in 2 billions of roubles annually. 
The large practical significance of an applied statistician justifies expediency of realization of activities on its methodology, in which this area of scientific and applied activity would be considered as whole, " from altitude of the bird's flight ". To have a capability of arguing of the tendencies of development of statistical methods, briefly we shall consider their history.
2. About a history of an applied statistician
The standard examples of an early stage(phase) of application of statistical methods are circumscribed in Shabby Завете (see, for example, Book of Numbers). From a mathematical point of view they were reduced to counts of number of hits of values of observable indications in certain gradation. Hereinafter outcomes begun to represent as _______________________________________ ______________
	 1РОССИЙСКАЯ association of statistical methods.
2РАБОТА is executed(made) at support of Russian fund of fundamental researches (project 97-06-80033). 
Tables and diagrams, as it and now does(makes) Госкомстат Russian Federation. It is necessary to recognize, that on a comparison with Shabby Заветом there is a progress - in Библии there were no tables. However there is no promoting on a comparison with activities russian статистиков of the end nineteenth - beginning of the twentieth century (standard monography of those times it is possible to consider(count) the book [11], which now ещ ё is easily accessible).
At once after origin of a theory of probabilities (Паскаль, Fermat, 17 centuries) probabilistic models of steel to be used at processing of the statistical data. For example, the frequency of birth of boys and girls was studied, the difference of probability of birth of a boy from 0.5 was established(installed), the reasons that, that in paris shelters this probability not that, that in Paris, etc were analyzed(analysed). There are many publications on a history of a theory of probabilities, however in some from them there are inexact statements(confirmation), that has forced the academician Ukrainian АН Б.В.Гнеденко to include in the last issuing of the rate(course) [12] chapter on a history of mathematics random. 
In 1794 (under other data - in 1795) К.Гаусс has developed a method of least squares, one from the most popular nowadays statistical methods, and has applied it at calculation of orbit астероида Церера - to struggle with errors of astronomical supervision(observations) [13]. In Х1Х century the noticeable contribution to development of a practical statistician was introduced бельгиец by(with) the Quetelet, because of of analysis of large number of the actual data shown stability(immunity) of relative statistical parameters(indexes), such, as a long of suicides among all death [14]. It is interesting, that the main(basic) ideas of the statistical acceptance control and certification of products were considered by the academician by the Bunyakovskii and were applied in russian army ещ ё in a middle Х1Х in. [15]. The statistical methods of quality management, certification and classification of production are now rather actual [16].
The present stage of development of an applied statistician can be counted since 1900, when the Englishman К.Пирсон is based the log-book "Biometrika". The first third ХХ in. Has passed in an athmosphere of a parametric statistician. The methods based on the analysis of the data from parametric sets of distributions, circumscribed by a curve set Пирсона were studied. Most popular was normal (Gaussian) distribution. For a test of hypothesis the criterions Пирсона, Стьюдента, Фишера were used. Were offered a method of a maximum probability, analysis of variance, the main(basic) ideas of planning of experiment are formulated. 
Developed in the first third ХХ in. The theory we shall name as a parametric statistician, as its main(basic) object of study are samples of distributions circumscribed by one or small number of parameters. Most general(common) is the set curve Пирсона, assigned in four parameters. As a rule, it is impossible to indicate any weighty reasons, on which the particular distribution of outcomes of supervision(observations) should enter(include) in that or other parametric set. The eleminations are well known(!known): if the probabilistic model provides toting independent aleatory variables, the sum is natural for describing by normal distribution; if in model the product of such sizes, the total, probably, приблтжается логарифмически by normal distribution, etc is considered. However in overwhelming majority of actual situations of similar models there are no , and approach(approximation) of actual distribution with the help of curve of a set Пирсона or it subfamilies - purely formal operation. 
Just from such reasons the academician С.Н.Бернштейн in 1927 in the report on All-Russia congress of mathematicians [17] criticized a parametric statistician. However this theory, infortunately, until now remains by the basis(fundamentals) of teaching of statistical methods and continues to be used in main(basic) weight прикладников, remaining by far from new trends in a statistician. Why so happens? To try to answer this problem(!on), we are converted to наукометрии. 
3. Наукометрия of an applied statistician 
Conducted some years back analysis of an applied statistician as areas scientific - practical of activity has shown, in particular(personally), that actual for the experts now are not less than 100 thousands of the publications (more in detail see articles [9,18,19]). Really each from us is familiar with essential(?much) by smaller quantity of the books and articles. So, in known(!known) трехтомнике Кендалла and Стьюарта [20-22] only about 2 thousands of the literary references. At the whole evidence of reasons about repeated duplication in the publications of valuable ideas it is necessary to recognize, that each expert in an applied statistician possesses only small part accumulated in this field of knowledge. Not surprised, that it is necessary constantly to collide with ignoring or recurring earlier obtained outcomes, with a drift in deadlock (from a point of view of practice) direction of researches, with feebleness at the reference(reversal) to the actual data, etc. All this - one from developments адапционного of the gear of braking of development of a science, about which 30 years back wrote В.В.Налимов and other науковеды (see, for example, [23]).
The conventional prejudice is, that each new outcome obtained by the contributor is a brick in a continuously growing building of a science, which will be indispensable  analysed and is used by scientific community. An actual situation - absolutely other. The basis(fundamentals) of professional knowledges of the contributor and engineer is included during training. Then they are filled up in that narrow direction, in which the expert works. The following stage(phase) - their duplicating to a new generation. In an outcome the high school text-books will defend from modern development on tens years. So, the text-books on a mathematical statistician, on our expert evaluation, in main(basic) correspond(meet) 40-60-м to years ХХ in. That is why to that to years there corresponds(meets) majority again of published researches and the more so - applied activities. Simultaneously it is necessary to recognize, that the outcomes not including in text-books, irrespective of their value almost everyone are overlooked.  
Development of deadlock directions actively proceeds. Psyhologically it is clear. I shall bring an example from the experience. In due course by the order Госстандарта I have developed methods of an evaluation of parameters a gamma - distribution [24]. Therefore to me are close and the activities on a parameter estimation on samples of distributions, inherings by that or other parametric sets, concept of a function of a maximum probability, efficiency(effectiveness) of assessments, use of an inequality Рао-Крамера etc are interesting. Infortunately, I know, that it - the deadlock branch, as the actual data are not subject to any parametric sets, is necessary to apply other statistical methods, about which the speech will go below. Is clear, that to the experts in the parametric statistician which has spent many years on perfecting in the area, psyhologically it is difficult to agree with this statement(confirmation). Including to me.
4. Point(!precisiouly) of growth(increase)
The domestic literature on an applied statistician so boundless, as well as world(global). Only in section " Mathematical methods of research " of the log-book " the Factory laboratory " since 1960-th years publishes more than 1000 articles. Let's not even try to enumerate collectives of the contributors or main(basic) monographies in this area (however, see article [19]). Let's mark only two issuings. Under my judgement, the best domestic book on an applied statistician is the collection of the statistical tables Л.Н.Большева and Н.В.Смирнова [25] with the in-depth comments playing a role of a text-book and a manual. Widespread three-that reference work [26-28] under edition С.А.Айвазяна is contained the useful information on many directions of an applied statistician. However in an account there are rather many errors, therefore to use the books [26-28] it is necessary with caution. 
The main(basic) purpose of the present article - to select(allocate) and to discuss " points(!precisiouly) of growth(increase) " of an applied statistician, those it of a direction, which are represented perspective hereafter, but while are removed on a background by conventional statements. 
Some years back at the description of a present stage of development of statistical methods by us were chosen [29 five actual directions, in which the modern applied statistician, i.e. five " of points(!precisiouly) of growth(increase) " develops: непараметрика, робастность, бутстреп, interval statistician, statistician of objects of a non-numerical nature. Let's discuss them. 
5. Nonparametric statistician
In the first third ХХ in., simultaneously with a parametric statistician, in activities Спирмена and Кендалла there were first nonparametric methods based on index of cograduations, carrying nowadays names these статистиков. But непараметрика, not doing(making) of the unrealistic suppositions that the cumulative distribution function of outcomes of supervision(observations) belong to that or other parametric sets of distributions, has become a noticeable part of a statistician only with the second third ХХ centuries. Per 30 years there were activities А.Н.Колмогорова and Н.В.Смирнова, offering and изучивших statistical criterions carrying now their names (a history of these activities explicitly is circumscribed in the article [30]). These criterions are based on use of so-called empirical process - differences between empirical and theoretical cumulative distribution functions multiplied on a square root from a sample size. In activity А.Н.Колмогорова 1933. The limiting(marginal) distribution of a supremum of a module of empirical process called now as a criterion Колмогорова is investigated. Then Н.В.Смирнов investigated a supremum and infimum of empirical process, and also integral (on a theoretical cumulative distribution function) guadrate of empirical process. 
 It is necessary to mark, that meeting sometimes in the literature [31] word collocations " the criterion Колмогорова-Смирнова ", as explicitly is justified in article [30], is incorrect, as these two statisticians were never printed together and did not study the same criterion. The combination " a criterion of a type Колмогорова-Смирнова ", used for a label of criterions, based on use of a supremum of functions from empirical process is correct 
After the second world(global) war the development of a nonparametric statistician went by fast rates. A large role the activities Вилкоксона and it of school have played. To the present time with the help of of nonparametric methods it is possible to decide practically same circle of statistical problems, as with the help of parametric [31]. The increasing role ишрают nonparametric evaluations of density, нерараметрические methods of a regression and pattern recognition (discriminant analysis). In our country the nonparametric methods have received rather large popularity after an output(exit) in 1965 of the first issuing of the mentioned above collection of the statistical tables Л.Н.Большева and Н.В.Смирнова [25], containing an in-depth table for main(basic) nonparametric criterions. 
Nevertheless parametric methods вс ё are even more popular nonparametric, especially among those прикладников, who is poorly familiar with statistical methods. Repeatedly were published (see reports in [4, 32]) experimental data which are indicative that the distributions of really observable aleatory variables, in particular(personally), measurement errors, in overwhelming majority of cases are excellent(different) from normal (гауссовских). Nevertheless theorists continue to build and to study statistical models based on гауссовости, and practice - to apply similar methods and models. In other words, " search under a lantern, instead of there, where have lost ".
6. Stability(immunity) of statistical procedures (робастность) 
If in parametric statements on the data the too rigid requirements - their cumulative distribution function are superimposed should belong to a certain parametric set, in nonparametric, on the contrary, too much weak - it is required only, that the cumulative distribution function were continuous. Thus the a priori information is ignored on what " a provisional kind " distributions. Априори it is possible to expect, that the account(record-keeping) it " of a provisional kind " will improve parameters(indexes) of quality of statistical procedures. Development of this idea is the theory of stability(immunity) (робастности) of statistical procedures, in which it is supposed, that the distribution of input datas differs from some parametric set a little. Since 60-th years this theory was developed П.Хубер [33], Ф.Хампель [34] and many by(with) other. From the monographies in Russian, treating about робастности and stability(immunity) of statistical procedures, early and most general(common) was the book [35], following(вnext) - monography [36]. Particular cases of a realization of idea робастности (stability)((immunity)) of statistical procedures are considered below statistician of objects of a non-numerical nature and interval statistician. 
There is a large variety of models робастности depending on that, which deviations(rejections) from a specific parametric set are supposed. Most popular [33,34] has appeared model of lets, in which the initial sample "gets littered" with small number of "lets" have in essence other distribution. However this model is represented "deadlock", as in most cases large lets or are impossible because of boundedness of a dial of the device, or it is possible to be saved of them, applying only statisticians constructed by a central part of a variational number(series). Besides in similar морделях frequency of clogging usually is considered known(!known), that in a combination with said does(makes) them малопригодными for practical use above.
More perspective the model Ю.Н.Благовещенского [37] is represented, in which the distance(span) between distribution of each sample unit and base distribution does not exceed a specific small. 
7. Бутстреп (duplication выборок)
Other from the mentioned above directions - бутстреп - is connected to heavily use of capabilities of computer facilities. The main(basic) idea is, that theoretical research should to replace by computing experiment. Instead of the description of sample by distribution from a parametric set we create large number "similar" выборок, i.e. is "multiplied sample. Then instead of an estimation of the characteristics both parameters and test of hypothesis because of of properties of a parent distribution is soluble these problems by a computing method, calculating statisticians, interesting for us, on each from "similar" выборок and analyzing(analysing) distributions, obtained at it. For example, instead of by a theoretical way to find distribution of a statistician, fiducial intervals and other characteristics, simulate much выборок, similar on initial, calculate appropriate values of a statistician, interesting for the contributor, and study their empirical distribution. The quantiles of this distribution set fiducial intervals, etc.
The term "бутстреп" instantly has received popularity after first the articles Б.Эфрона 1979 [39] on this subjects. It(he) at once has become to be considered in weight of the publications, including popular scientific [40]. In " of Factory laboratory " the selection of the articles on бутстрепу [41] was located, the collection of the articles Б.Эфрона [42] is manufactured(issued). The main(basic) idea бутстрепа on Б.Эфрону is, that the Monte-Carlo method (statistical tests) multiply extracts(drawn) samples of empirical distribution. These samples, naturally, are versions initial, remind it. 
In itself idea " of a duplication выборок " was known(!known) much earlier. The article Б.Эфрона [39] is named so: " бутстреп-methods: a new sight on a method of a collapsible knife ". Mentioned " the method of a collapsible knife " (jackknife) is offered М.Кенуем in 1949, 30 years prior to the article of the article Б.Эфрона. " The Duplication выборок " thus implements a way by an elemination of one supervision(observation). Thus for sample of volume n n " similar " on it(her) выборок of volume (n - 1) each is obtained. If to exclude till 2 supervision(observations), the number "similar" выборок will increase up to n (n - 1) / 2 volumes (n - 2) each. 
The advantages and shortages бутстрепа as statistical method are considered in [43]. There and in [18] the information on a number(series) of similar methods is resulted. It is necessary to underline, that бутстреп on Эфрону [39-42] - only one from versions of methods " of a duplication of sample " (resampling), and, on our sight, not most successful. The method " of a collapsible knife " is represented more useful. On it the basis(fundamentals) can formulate the following simple practical recommendation.
Let's assume, that you on sample do(make) any statistical conclusions(injections). You want to learn(find out) also, as far as these conclusions(injections) are steady. If you have other (monitoring) samples circumscribing that appearance, you can apply to a Nim the same statistical procedure and to compare outcomes. And if such выборок are not present? Then you can them construct artificially. Take initial sample and exclude one element. Receive similar sample. Then return this element and exclude other. Receive the second similar sample. By acting(arriving) so with all elements of initial sample, receive so much выборок, similar on initial, what it volume. It is necessary to treat of their themes by a way, as initial, and to study stability(immunity) of obtained conclusions(injections) - spread(dispersion) of assessments of parameters, frequency of acceptance or deviation(rejection) of hypothesises etc. 
It is possible to change not sample, and data. As always there are errors of measurement, the actual data is not numbers, and intervals (outcome of measurement a plus - minus an error). The statistical theory of the analysis of such data is necessary.
8. Statistician of the interval data
Perspective and fast developing direction of the last years - mathematical statistician of the interval data. The speech goes about development of methods of a mathematical statistician in a situation, when the statistical data - not numbers, and intervals, in particular(personally), induced by imposing(superposition) of measurement errors on values of aleatory variables. The obtained outcomes are reflected, in particular(personally), in performances(statements) on conducted in " of Factory laboratory " controversies [44] and in the reports of international conference ИНТЕРВАЛ-92 [45].
The statistician of the interval data conceptually is connected to interval mathematics, in which in a role of numbers the intervals (see, for example, monography [46]) act. This direction of mathematics is further development by all of known rules of approximate evaluations devoted expression of errors of a sum, difference, product, individual(private) through errors of those numbers, above which the listed(transferred) operations implement. As it is visible from the reports [45], to the present time it was possible to decide, in particular(personally), number(series) of problems of the theory of interval differential equations, in which factors, entry conditions and the solutions are described with the help of of intervals. 
The leading scientific school in the field of a statistician of the interval data is a school проф. А.П.Вощинина, actively working with the end of 70-th years. The obtained outcomes are reflected in a number(series) of the monographies (see, in particular(personally), [47,48,49]), articles [44], reports [45], thesises [50,51]. In particular(personally), the problems регрессионного of the analysis, planning of experiment, comparison of alternatives and decision making in conditions of interval uncertainty are investigated.
Let's consider other direction in a statistician of the interval data, which also is represented perspective. In it(him) the asymptotic methods of a statistical analysis of the interval data develop at large volumes выборок and small errors of measurements. In difference from a classical mathematical statistician, sample size at first directs to infinity and only then - up to zero of an error decreases. In particular(personally), with the help of of such asymptotics the rules of selection of a method of a parameter estimation a gamma - distribution in ГОСТ 11.011-83 [24] were formulated.
In development of ideas formulated in [52,53], the general(common) scheme of research including calculation нотны (of the greatest possible deviation(rejection) of a statistician is developed, called интервальностью of input datas) and rational sample size (which excess does not give essential increase of accuracy of an estimation). She(it) is applied to an estimation of expectation, dispersion, factor of a variation, parameters a gamma - distribution and characteristics of additive statisticians, at a test of hypothesis about parameters of normal distribution, including with the help of of criterion Стьюдента, and also hypothesis of uniformity(homogeneity) with the help of of criterion Смирнова. The approaches to consideration of the interval data in main(basic) statements регрессионного, discriminant and cluster analyses are developed. In particular(personally), the influence of errors of measurements and supervision(observations) on properties of algorithms регрессионного of the analysis is investigated, the ways of calculation нотн and rational volumes выборок are developed, are entered and the new concepts many-dimensional and asymptotic нотн are investigated, the appropriate limiting(marginal) theorems are proved. The development of the interval discriminant analysis is begun, in particular(personally), the influence интервальности of the data on a parameter,(index,) entered by us, of quality of a classification is considered. The asymptotical behavior of assessments of a method of moment and maximum likelihood estimates (and also more general(common) - assessments of minimum contrast) is investigated, the asymptotic comparison of these methods is conducted in case of the interval data. The general conditions are found, at which, in difference from a classical mathematical statistician, the method of moment gives precisiouly evaluations, than method of a maximum probability (see. Article [54], in which are adduced иакже of the reference to other publications relating a considered direction in a statistician of the interval data).. 
As has shown, in particular(personally), the international conference ИНТЕРВАЛ-92, in the field of an asymptotic mathematical statistician of the interval data a russian science has world(global) priority. The deployment of activities on considered subjects will allow to fix this priority to receive theoretical outcomes establishing in new area of a mathematical statistician and necessary for justified statistical analysis almost of all data types, necessary For algorithms of an interval statistician "parallel" usually used algorithms of an applied mathematical statistician should be included inied statistical analysis kinds of the statistical software. It will allow in an obvious kind to take into account availability of errors at outcomes of supervision(observations) to pull together items метрологов and статистиков.

9. Statistician of objects of a non-numerical nature 
As a part of an applied statistician
According to a classification of statistical methods adopted in [55-56], the applied statistician is divided into the following four areas:
Statistician (numerical) aleatory variables,
Many-dimensional statistical analysis, 
Statistician of time series and random processes, 
Statistician of objects of a non-numerical nature.
First three from these areas are classical. Let's stay on fourth, only some more included in mass consciousness of the experts. It name also by statistician of the non-numerical data or simply by non-numerical statistician.
The initial object in a mathematical statistician is a sample. In the probabilistic theory of a statistician the sample is a set(combination) of the independent uniformly distributed stochastic elements. What nature of these elements? In a classical mathematical statistician (that, that sample units usually teach to the students) are numbers. In a many-dimensional statistical analysis - vector. And in a non-numerical statistician the sample units are objects of a non-numerical nature, which cannot be be to be combined and multiply on numbers. In other words, the objects of a non-numerical nature lie in the spaces which are not have to a vectorial structure.
Examples of objects of a non-numerical nature are (see also reviews [56-57]):
Values of qualitative indications, i.e. outcomes of the coding of objects with the help of of specific list of categories (gradation); 
Ordering (rangings) by the experts is exemplar of production (at an evaluation е ё of a technological level and competitiveness)) or applications for realization of scientific activities (at realization of competitions on allocation грантов);
Classifications, i.e. partition of objects on groups similar among themselves (clusters);
Tolerances, i.e. binary attitudes(relations) circumscribing a likeness of objects among themselves, for example, likeness of subjects of scientific activities estimated by the experts with the purpose of rational formation of expert advices(councils) inside certain area of a science;
Outcomes of conjugate comparisons or quality control of production on an alternate indication ("годен" - "reject"), i.e. sequence from 0 and 1; 
Sets (usual or indistinct), for example, zones hit with corrosion, or lists of the possible(probable) reasons of emergencies composed by the experts is independent from each other;
Words, proposals, texts;
Vector, which coordinate(co-ordinates) - set(combination) of values of varied indications, for example, outcome of compiling of the accounts about scientific and technical activity (form(shape) No.1-наука) or completed computer-controlled history of illness, in which the part of indications has qualitative character, and part - quantitative;
The answers to problems(!on) of the expert, marketing or sociological questionnaire, part which from has the quantitative character (is possible, interval), the part is reduced to selection by one from the several helps, and the part represents the texts; etc.
The interval data (see are higher) too it is possible to consider as an example of objects of a non-numerical nature, namely, as a particular case of indistinct sets.
From a beginning of 70-th years under influence of the inquiries of applied researches in technical, medical and socio economic sciences in Russia a statistician of objects of a non-numerical nature known(!known) as well as a statistician of the non-numerical data or non-numerical statistician actively develops. In creation of this rather new area of an applied mathematical statistician the priority belongs to the russian scientists.
Large role the scientific seminar, based in 1973, " Expert evaluations and analysis of the data " has played. Per 60 years the soviet scientific community has become to be interested in methods of expert assessments (about their history and state -of-the-art see review [58]). As the corollary, was begun familiarity with particular математизированными by the theories connected to these methods. The speech goes about the representative theory of measurements becoming known(!known) in our country on the article,!known in our country, Зинеса in the collection [59] and book И.Пфанцагля [60], about the theory of an illegibility Л.А.Заде [61], theory of conjugate comparisons circumscribed in the monography Г.Дэвида [62]. To this circle of ideas adjoin the theory of random sets (see, for example, the book Ж.Матерона [63]) and the methods many-dimensional шкалирования (are circumscribed in the monographies А.Ю.Терехиной [64] and В.Т.Перекреста [65]). But the greatest influence was rendered by(with) ideas Дж. Кемени, which аксиоматически has entered a distance(span) between rangings (now it is named in the literature by a distance(span) Кемени) and has offered to use as an average the solution of an optimization problem (now - median Кемени). It the modest book [66], written in the co-authorship with Дж. Снеллом, has generated a large flow of researches. 
Within 70-th years because of of inquiries of the theory of expert assessments (and also sociology, economy, engineering and the medicine) developed particular directions of a statistician of objects of a non-numerical nature. The communications(connection,binder) between particular kinds of such objects were established(installed), the probabilistic models (see review [67]) are developed for them. The totals of this period are bringed in the monographies [35,68,69]).
The following stage(phase) - allocation of a statistician of objects of a non-numerical nature as an independent direction in an applied statistician, which kernel are the methods of a statistical analysis of the data of any nature. The program of development of this new scientific direction for the first time was formulated in article [70]. The realization of this program was realized per 80 years. The concentration on internal problems of a non-numerical statistician is characteristic of activities of this period. The references to the particular monographies, collections, articles and other publications of several tens authors are adduced in the reviews [56,57,67]. Let's mark only collection [71], specially to devoted non-numerical statistician, and thesis [72], relating to the nonparametric theory of conjugate comparisons.
To 90-м to years the statistician of objects of a non-numerical nature from a theoretical point of view was enough well advanced, main(basic) ideas, the approaches and methods were developed and are investigated mathematically, in particular(personally), many theorems are proved. However she(it) remained unsufficiently апробированной in practice. It was connected both to its comparative youth, and with well-known singularities of organization of a science per 80 years, when there were no sufficient stimulus by, that the theorists were took by broad introduction of the outcomes. And per 90 years the time from математико-statistical researches has set in to proceed(pass) to application of obtained outcomes in practice. This tendency is well reflected in the monographies [73,74], materials of international conference " Management(control) large systems " [75].
It is necessary to mark, that in a statistician of objects of a non-numerical nature, as well as in other areas of an applied mathematical statistician and applied mathematics generally, the same mathematical scheme can with success be applied and in technical researches, both in medicine, and in sociology, and for the analysis of expert assessments, that is why it is best be for formulating and for studying in a most general view, for objects of any nature. 
10. Main(basic) ideas of a statistician of objects of a non-numerical nature
In what basic novelty of a non-numerical statistician? The operation of addition is characteristic of a classical mathematical statistician. At calculation of the selective characteristics of distribution (selective mean arithmetical, selective dispersion etc.), in регрессионном the analysis and other areas of this scientific discipline the sums are constantly used. The mathematical vehicle - laws of large numbers, Central limiting(marginal) theorem and other theorems - are aimed at study of sums. In non-numerical the statistician cannot use operation of addition, as the sample units lie in the spaces, where there is no operation of addition. The methods of processing of the non-numerical data are based on basic other mathematical vehicle - on application of various distances(spans) in the spaces of objects of a non-numerical nature.
Briefly we shall consider some ideas developed in a statistician of objects of a non-numerical nature for the data, lying in the spaces of any kind. The classical problems of a datadefinition, estimation, test of hypothesis - but for the nonclassical data, that is why by nonclassical methods are decided.  
By first we shall discuss a problem of definition(determination) of averages. Within the framework of the representative theory of measurements it is possible to indicate a kind of averages appropriate of themes or other dials of measurement [35]. In a classical mathematical statistician of averages introduce with the help of of operations of addition (selective mean arithmetical, expectation) or ordering (selective and theoretical median). In the spaces of any nature of average value it is impossible to define(determine) with the help of operations of addition or ordering. Theoretical and empirical mean it is necessary to introduce as the solution of extremum problems. For theoretical mean it - the problem of minimization of expectation (in a classical sense) distance(span) from a stochastic element with values in considered space up to a fixed point(!precisiouly) of this space (is minimized the indicated function from this point(!precisiouly)). For empirical mean expectation undertakes on empirical distribution, i.e. The sum of distances(spans) from some point(!precisiouly) up to sample units and undertakes then is minimized on this point(!precisiouly). Thus both empirical, and theoretical mean as the solutions of extremum problems can be a not unique element of space, and to consist of a set of such elements, which can appear and empty. Nevertheless it was possible to formulate and to provick the laws of large numbers for the averages determined by an indicated image, i.e. to place(install) convergence empirical mean to theoretical.
Has appeared, that the methods of a proof of the laws of large numbers suppose much more broad area of application, than that, for which they were developed. Namely, it was possible to study an asymptotics of the solutions of extreme statistical problems, by which, as is known, the majority of statements of an applied statistician [26] is reduced. In particular(personally), except the laws of large numbers the competence of assessments of minimum contrast, including maximum likelihood estimates and робастных of assessments is established(installed) also. To the present time the similar evaluations are investigated as well in an interval statistician.
In a statistician in the spaces of any nature the large role is played by(with) nonparametric evaluations of density used, in particular(personally), in various algorithms регрессионного, discriminant, cluster analyses. In a non-numerical statistician is offered and a number(series) of types of nonparametric assessments of density in the spaces of any nature is investigated, in particular(personally), their competence is proved, the speed of convergence is investigated and the remarkable fact of concurrence(coincidence) of the best speed of convergence in any case with that is established(installed) which has to be in the classical theory for numerical aleatory variables.
Discriminant, cluster, регрессионный the analyses in the spaces of any nature are based or on the parametric theory - and then the approach connected to an asymptotics of the solution of extreme statistical problems - or on the nonparametric theory - and then is applied the algorithms because of of nonparametric assessments of density are used.
For a test of hypothesis the statisticians of an integral type, in particular(personally), type омена-guadrate can be used. It is curious, that the limiting(marginal) theory of such statisticians constructed originally in classical statement [76], has gained natural (completed, refined) a kind just for the spaces of any kind [77], as thus it was possible to conduct reasoning, leaning on base mathematical ratioes, instead of on those individual(private) (from a generic point of sight), that were connected to finite-dimensional space.
The outcomes connected to particular areas of a statistician of objects of a non-numerical nature, in particular(personally), with a statistician of indistinct sets [78] are of interest, with random sets [35] (it is necessary to mark, that the theory of indistinct sets in a certain sense is reduced to the theory of random sets [35,78]), with the nonparametric theory of conjugate comparisons [72], with axiomatic introduction of the metrics in the particular spaces of objects of a non-numerical nature [71].  
For the analysis non-numerical, in particular(personally), expert data the discriminatory analysises are rather important. On the other hand, it is most natural to put and to decide problems of a classifications based on use of distances(spans) or parameters(indexes) of distinction(difference), within the framework of a statistician of objects of a non-numerical nature. It concerns as a pattern recognition with the teacher (in other words, discriminant analysis), and pattern recognition without the teacher (i.e. cluster analysis). The state -of-the-art discriminant and cluster analysis from a point of view of a statistician of objects of a non-numerical nature is reflected activities in [79].
The statistical methods of the analysis of the non-numerical data especially are well adapted to application in economy, sociology and expert evaluations, as in these areas from 50 % up to 90 % of the data are non-numerical [80].
11. Inference
We have considered five " of points(!precisiouly) of growth(increase) " of an applied statistician as methodical discipline. Certainly, they do not reach(settle) the whole variety(varieties) of front of scientific researches in this area. In particular(personally), all problems posed at the end of 70-th years in so-called " цахкадзорской тетради " [81] are decided(solved) by no means. Besides we did not affect almost not diverse applications of statistical methods in particular application areas. It is a lot of interesting problems is in a design of experiments, especially kinetic (see, for example, article [2,82]), at the analysis of problems of a reliability (see, in particular(personally), article [83]), in new statistical methods of product quality control, including in connection with ideas Г.Тагути (see about it article [84]), in problems(!on) of an ecology and safety [75], и.др. 
During last more than 60 years in Russia are observed a huge gap between a state statistician and scientific community of the experts on statistical methods (more in detail about it see [19]). In a text-book on a history of a statistician [14] the names of terms - correspondents АН USSR Н.В.Смирнова and Л.Н.Большева are not mentioned at all! Therefore there is nothing surprising that the tendencies of development of a modern applied mathematical statistician so are considered by the domestic authors, as well as it a history a little. I shall be glad, if the present article will put a beginning of a controversy about the future of our science. 

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