Name
Orlov Alexander Ivanovich
Scholastic degree
•
•
•
Academic rank
professor
Honorary rank
—
Organization, job position
Bauman Moscow State Technical University
Web site url
—
Articles count: 155
One of the "points of growth" of applied statistics is
methods of reducing the dimension of statistical
data. They are increasingly used in the analysis of
data in specific applied research, such as sociology.
We investigate the most promising methods to
reduce the dimensionality. The principal
components are one of the most commonly used
methods to reduce the dimensionality. For visual
analysis of data are often used the projections of
original vectors on the plane of the first two
principal components. Usually the data structure is
clearly visible, highlighted compact clusters of
objects and separately allocated vectors. The
principal components are one method of factor
analysis. The new idea of factor analysis in
comparison with the method of principal
components is that, based on loads, the factors
breaks up into groups. In one group of factors, new
factor is combined with a similar impact on the
elements of the new basis. Then each group is
recommended to leave one representative.
Sometimes, instead of the choice of representative
by calculation, a new factor that is central to the
group in question. Reduced dimension occurs during
the transition to the system factors, which are
representatives of groups. Other factors are
discarded. On the use of distance (proximity
measures, indicators of differences) between
features and extensive class are based methods of
multidimensional scaling. The basic idea of this
class of methods is to present each object as point of
the geometric space (usually of dimension 1, 2, or 3)
whose coordinates are the values of the hidden
(latent) factors which combine to adequately
describe the object. As an example of the
application of probabilistic and statistical modeling
and the results of statistics of non-numeric data, we
justify the consistency of estimators of the dimension of the data in multidimensional scaling,
which are proposed previously by Kruskal from
heuristic considerations. We have considered a
number of consistent estimations of dimension of
models (in regression analysis and in theory of
classification). We also give some information about
the algorithms for reduce the dimensionality in the
automated system-cognitive analysis
Statistical methods are widely used in domestic
feasibility studies. However, for most managers,
economists and engineers, they are exotic. This is
because modern statistical methods are not taught in
the universities. We discuss the situation, focusing
on the statistical methods for economic and
feasibility studies, ie, econometrics. In the world of
science, econometrics has a rightful place. There are
scientific journals in econometrics, Nobel Prizes in
Economics are awarded to series of researches in
econometrics. The situation in the field of scientific
and practical work and especially the teaching of
econometrics in Russia is disadvantaged. Often,
individual particular constructions replace
econometrics in general, such as those related to
regression analysis. In econometrics we select three
types of scientific and applied activities:
development and study of methods of applied
statistics, taking into account the specifics of
economic data; development and study of
econometric models, in accordance with the specific
needs of economic science and practice; the use of
econometric methods for statistical analysis of
specific economic data. This article describes these
three types of scientific and applied activities. We
discuss the specificity of economic data. We show
the importance of economic non-numeric values. We
discuss the statistics of interval data - scientific
direction at the joint of metrology and statistics. We
give the representation of the econometric models.
Problems of application of econometric methods are
considered as an example of inflation. We discuss
the statistics and econometrics as the field of
scientific and practical activities. We have examined
econometric methods in practical and training
activities
The founder of the economic theory is Aristotle.
The so-called "market economy" is a perversion of
Aristotle's views. We have to eliminate distortions.
What can replace the "market economy"? We are
developing a new organizational-economic theory -
solidary information economy, based on the views
of Aristotle. The name of this theory has changed
over time. Initially, we used the term "nonformal
information economy of the future", and then
began to use the term "solidary information
economy." In connection with Biocosmology and
neo-Aristotelism preferred is an adequate term
"functionalist organic information economy". This
article describes the main provisions of solidary
information economy, intended to replace the
market economy as a management tool. The main
problems are discussed, the solution of which is
devoted to research related to the considered basic
organizational and economic theory. We discuss
Aristotle's positions, on which the economic theory
is based, in particular, solidary information
economy. We prove that the market economy has
remained in the XIX century and the mainstream in
modern economic science - justification of
insolvency of a market economy and the need to
move to a planned system of economic
management. We examine the impact of ICT on
economic activity. We develop the approaches to
decision-making in the solidary information
economy. On the basis of modern decision theory
(especially expert procedures) and informationcommunication
technologies people can get rid of
chrematistics and will understand the term of
"economy" according to Aristotle
In accordance with the new paradigm of mathematical statistics the statistics of objects of nonnumerical nature (statistics of nonnumerical objects, non-numerical data statistics, non-numeric statistics) is one of the four main areas of mathematical statistics. Statistics of objects of nonnumerical nature consists of a central core - statistics in spaces of arbitrary nature - and statistical theories of analysis of specific types of non-numeric data. To identify possibilities of application of statistics of objects of nonnumerical nature it is useful to explore the multiformity of objects of non-numeric nature. This is the subject of this article. We have considered the results of measurements at scales other than absolute; binary relations; dichotomous (binary) data; sets. We have also analyzed the objects of non-numerical nature as statistical data, and their importance in the formation of statistical or mathematical model of a real phenomenon, as a result of data analysis
We introduce the concept of "controlling organizational-economic methods". We define the terms in the sequence "the problem - the model - the method - the conditions of applicability". We have described the basic organizational-economic model of industrial firm; by means of this model we have discussed the problems of development of modern organizational-economic methods. We have demonstrated the relevance of the theory and methodology of organizational-economic modeling. For example, we consider the application of statistical methods at various stages of the life cycle of the product, the problem of internal risks in an industrial firm and accounting for inflation in the analysis of activities of the organization
The article is devoted to the methods of analysis of statistical and expert data in problems of economics and management that are discussed in the framework of scientific specialization "Mathematical methods of economy", including organizational-economic and economic-mathematical modeling, econometrics and statistics, as well as economic aspects of decision theory, systems analysis, cybernetics, operations research. The main provisions of the new paradigm of this scientific and practical field are developed by the author of this article in the 1980s during the creation of the All-Union Statistical Association. The new paradigm is compared with the old (corresponding to the middle of XX century). Is summarized monographs, textbooks and manuals prepared under the leadership of the author of this paper in the XXI century according to the new paradigm
In 1979, non-numerical data statistics was singled out as an independent area of applied statistics. Initially, the term "statistics of objects of non-numerical nature" was used to denote this area of mathematical methods of economics. Our basic non-numeric statistics textbook is called "Non-Numeric Statistics". Non-numerical data statistics is one of the four main areas of applied statistics (along with number statistics, multidimensional statistical analysis, statistics of time series and random processes). Statistics of non-numerical data are divided into statistics in spaces of a general nature and sections devoted to specific types of non-numerical data (statistics of interval data, statistics of fuzzy sets, statistics of binary relations, etc.). Currently, statistics in spaces of a general nature is the central part of applied statistics, and non-numeric data statistics including it is the main area of applied statistics. This statement is confirmed, in particular, by the analysis of publications in the section "Mathematical Research Methods" of the journal "Industrial Laboratory. Diagnostics of Materials" - the main place of publication of russian studies on applied statistics. This article is devoted to the analysis of the basic ideas of non-numerical data statistics against the background of the development of applied statistics from the perspective of a new paradigm of mathematical research methods. Various types of non-numeric data are described. The historical path of statistical science is analyzed. We have discussed the development of statistics of non-numerical data. The article analyzes basic ideas of statistics in spaces of a general nature: average values, laws of large numbers, extreme statistical problems, nonparametric estimates of the probability density, classification methods (diagnostics and cluster analysis), statistics of the integral type. Some statistical methods for analyzing data lying in specific spaces of non-numeric nature are briefly considered: non-parametric statistics (real distributions usually differ significantly from normal), statistics of fuzzy sets, theory of expert estimates (the Kemeny median is a sample average of expert orderings), etc. We have also discussed some unsolved problems in statistics of nonnumeric data
In many applications, we study the time series (or a
random process), which is the sum of the periodic
deterministic function of time and random errors that
distort the periodic signal. It is required to estimate
the length of the period and the periodic component.
It does not assume that the periodic function is
included in any parameter family of functions, such
as finite sums of sines and cosines. It is obvious that
the assumption of occurrence of a periodic function
in parametric family does not meet the
characteristics of the real world, ie, is conditional,
internal mathematical (look for the keys under the
lamp because there is a light, not in the bush, where
lost, because there are dark). For similar reasons, it
is impossible to assume that the distribution function
of the random errors is included in any parameter
family of distributions. In accordance with the new
paradigm of mathematical statistics in this article we
studied the problem of nonparametric estimation
(minimum) length of the period and the periodic
component of the signal. On the basis of natural
variation and scope of indicators is suggested a new
class of nonparametric estimators of the length of the
period and the periodic component in the time
series. Based on the general results of statistics of
objects of non-numeric nature we proved the
consistency of these estimates. From the practical
point of view it is necessary to minimize the
numerical (one parameter - ability length of period
of time) one or more of the 66 functionals, described
in the article
We continue the series of articles about the history of statistics. We discuss the development of nonparametric and applied statistics in our country in 1930 - 1980 years. We have presented the studies of the great statisticians of the twentieth century, such as N.V. Smirnov, L.N. Bolshev, V.V. Nalimov. American statistics show Russian debate about applied statistics. We have briefly listed the
process of creation of the All-Union Statistical Association (1990) and its further developments
The article is devoted to the nonparametric point and
interval estimation of the characteristics of the
probabilistic distribution (the expectation, median,
variance, standard deviation, variation coefficient) of
the sample results. Sample values are regarded as the
implementation of independent and identically
distributed random variables with an arbitrary
distribution function having the desired number of
moments. Nonparametric analysis procedures are
compared with the parametric procedures, based on
the assumption that the sample values have a normal
distribution. Point estimators are constructed in the
obvious way - using sample analogs of the
theoretical characteristics. Interval estimators are
based on asymptotic normality of sample moments
and functions from them. Nonparametric asymptotic
confidence intervals are obtained through the use of
special output technology of the asymptotic relations
of Applied Statistics. In the first step this technology
uses the multidimensional central limit theorem,
applied to the sums of vectors whose coordinates are
the degrees of initial random variables. The second
step is the conversion limit multivariate normal
vector to obtain the interest of researcher vector. At
the same considerations we have used linearization
and discarded infinitesimal quantities. The third step
- a rigorous justification of the results on the
asymptotic standard for mathematical and statistical
reasoning level. It is usually necessary to use the
necessary and sufficient conditions for the
inheritance of convergence. This article contains 10
numerical examples. Initial data - information about
an operating time of 50 cutting tools to the limit
state. Using the methods developed on the
assumption of normal distribution, it can lead to
noticeably distorted conclusions in a situation where
the normality hypothesis failed. Practical
recommendations are: for the analysis of real data we
should use nonparametric confidence limits