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
The general scheme of modern statistical science is
just like this. Mathematical Statistics is a part of
mathematics that studies the statistical structure (it
itself does not give recipes analysis of statistical
data, however, it is developing methods that are
useful for use in theoretical statistics). Theoretical
Statistics - the science dedicated to the models and
methods of analysis of concrete statistical data.
Applied Statistics (in the narrow sense) is devoted to
the statistical techniques of data collection and
processing (it includes the methodology of statistical
methods, the organization of sample surveys, the
development of statistical techniques, the creation
and use of statistical software). Applications of
statistical methods in concrete fields (in economics
and management - Econometrics, in biology -
Biometrics, in chemistry - Chemometrics, in
technical research - Technometric, in geology,
demography, sociology, medicine, history, etc.).
Often positions 2 and 3 together are called Applied
Statistics. Sometimes position 1 is called Theoretical
Statistics. These terminological differences are
related to the fact that the above-described
development of the considered scientific and applied
field not once, not completely and not always
adequately reflected in the minds of experts.
Meanwhile, there are still textbooks of appropriate
level of representation of the mid-twentieth century.
The article analyzes the post-war development of
the national statistics. We have identified five
"growth points": nonparametrics, robustness,
bootstrap, statistics of interval data, and statistics of
non-numeric data. We have discussed content,
development and the basic ideas of statistics of nonnumeric
data. We have given a number of
unresolved problems of theoretical and applied
statistics
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 consider an approach to the transition from
continuous to discrete scale which was defined by
means of step of quantization (i.e. interval of
grouping). Applied purpose is selecting the number
of gradations in sociological questionnaires. In
accordance with the methodology of the general
stability theory, we offer to choose a step so that the
errors, generated by the quantization, were of the
same order as the errors inherent in the answers of
respondents. At a finite length of interval of the
measured value change of the scale this step of
quantization uniquely determines the number of
gradations. It turns out that for many issues gated it
is enough to point 3 - 6 answers gradations (hints).
On the basis of the probabilistic model we have
proved three theorems of quantization. They are
allowed to develop recommendations on the choice
of the number of gradations in sociological
questionnaires. The idea of "quantization" has
applications not only in sociology. We have noted,
that it can be used not only to select the number of
gradations. So, there are two very interesting
applications of the idea of "quantization" in
inventory management theory - in the two-level
model and in the classical Wilson model taking into
account deviations from it (shows that
"quantization" can use as a way to improve
stability). For the two-level inventory management
model we proved three theorems. We have
abandoned the assumption of Poisson demand,
which is rarely carried out in practice, and we give
generally fairly simple formulas for finding the
optimal values of the control parameters,
simultaneously correcting the mistakes of
predecessors. Once again we see the interpenetration
of statistical methods that have arisen to analyze
data from a variety of subject areas, in this case,
from sociology and logistics. We have another proof
that the statistical methods - single scientificpractical
area that is inappropriate to share by areas
of applications
The article begins with the letter of the chief
engineer of chemical plant near Moscow. He
requests to analyze of data by means of modern
statistical methods and give an opinion on the
presence (or absence) of the relationship between
the two methods of determining the viscosity of the
mastic. For each of the batches of mastic It was
presented two numbers - the viscosity measurement
results of the two methods. These numbers form two
paired samples. We want to install, give whether
two specific methods similar results. The true values
of viscosity in different batches are not equal. Their
difference is not allows us to combine the results of
the first measurement method in first sample, the
results of the second method - in the second sample,
as we can do in the case of testing the homogeneity
of two independent samples. For solutions to this
problem we discuss four statistical criterions, based
on a study of the differences between corresponding
values in two paired samples. We test the hypothesis
of equality 0 of median of these differences (sign
test) and of equality 0 of the mathematical
expectation of these differences. Hypothesis of
testing of equality of the distribution functions of
two paired samples is reduced to the hypothesis of
symmetry of the distribution function of these
differences with respect to 0. In the alternative of the
shift is proposed to use the Wilcoxon signed rank
criterion. In the total alternative is proposed to use
criterion of the omega-square type which is
developed by the author of this article
Nonparametric estimates of the probability
distribution density in spaces of arbitrary nature are
one of the main tools of non-numerical statistics.
Their particular cases are considered - kernel density
estimates in spaces of arbitrary nature, histogram
estimations and Fix-Hodges-type estimates. The
purpose of this article is the completion of a series
of papers devoted to the mathematical study of the
asymptotic properties of various types of
nonparametric estimates of the probability
distribution density in spaces of general nature.
Thus, a mathematical foundation is applied to the
application of such estimates in non-numerical
statistics. We begin by considering the mean square
error of the kernel density estimate and, in order to
maximize the order of its decrease, the choice of the
kernel function and the sequence of the blur
indicators. The basic concepts are the circular
distribution function and the circular density. The
order of convergence in the general case is the same
as in estimating the density of a numerical random
variable, but the main conditions are imposed not on
the density of a random variable, but on the circular
density. Next, we consider other types of
nonparametric density estimates - histogram
estimates and Fix-Hodges-type estimates. Then we
study nonparametric regression estimates and their
application to solve discriminant analysis problems
in a general nature space
Many procedures of applied mathematical statistics
are based on the solution of extreme problems. As
examples it is enough to name methods of least
squares, maximum likelihood, minimal contrast,
main components. In accordance with the new
paradigm of applied mathematical statistics, the
central part of this scientific and practical discipline
is the statistics of non-numerical data (it is also
called the statistics of objects of non-numerical
nature or non-numeric statistics) in which the
empirical and theoretical averages are determined by
solving extreme problems. As shown in this paper,
the laws of large numbers are valid, according to
which empirical averages approach the theoretical
ones with increasing sample size. Of great
importance are limit theorems describing the
asymptotic behavior of solutions of extremal
statistical problems. For example, in the method of
least squares, selective estimates of the parameters
of the dependence approach the theoretical values,
the maximum likelihood estimates tend to the
estimated parameters, etc. It is quite natural to seek
to study the asymptotic behavior of solutions of
extremal statistical problems in the general case.
The corresponding results can be used in various
special cases. This is the theoretical and practical
use of the limiting results obtained under the
weakest assumptions. The present article is devoted
to a series of limit theorems concerning the
asymptotics of solutions of extremal statistical
problems in the most general formulations. Along
with the results of probability theory, the apparatus
of general topology is used. The main differences
between the results of this article and numerous
studies on related topics are: we consider spaces of a
general nature; the behavior of solutions is studied
for extremal statistical problems of general form; it
is possible to weaken ordinary requirements of
bicompactness type by introducing conditions of the
type of asymptotic uniform divisibility
The term "methodology" is understood differently. Methodology - the doctrine of the organization. Methodology (from the "method" and "logy") - the doctrine of structure, logical organization, methods and means of action. Methodology - the system of principles and methods of organization and construction of theoretical and practical activities, as well as teaching on this system. From these definitions it follows that the methodology - is an intellectual base rod defining approach to specific activities to management decisions. The methodology, which adheres to the manager, lies at the heart of its activities, determines its success or failure, manifested in the consequences of decisions. We give some examples of methodological errors which lead to wrong management decisions. So, the person who seriously requires providing "maximum profit at minimum cost" should be classified into one of two classes, which can be briefly described as "fools" and "liars". Profit must not be the sole purpose of business. The following section will discuss the methodology in place of conducting various scientific economic and technical studies. A natural continuation of the topic - the wording of some of the methodological problems using mathematical methods
The actuality of ecological issues was realized about
50 years ago. The highlight of the ecological
movement to protect the environment has been, in
our estimation, the United Nations Conference on
Environment and Development (Rio de Janeiro,
1992), which adopted the concept of sustainable
development. After 1992 the interest in ecology of
broad masses was decreased slightly, although the
environmental problems are not only remained, but
appeared to a greater extent. However, now there is
a legal basis for their decisions. Particularly,
enterprises must have a certified environmental
management system; otherwise they will be unable
to compete in international markets. Awareness by
humanity of need for environmental protection has
led, in particular, to the deployment of scientific
research in the field of ecological safety studies.
Therefore, we have found that it is necessary and
useful to report about the research of our team on
this subject. Ecological security issues are highly
relevant to the energy sector, in particular for gas
enterprises. As an example of the new scientific
results we discuss the innovative approach to the
disposal of drilling waste. The basic idea - the use of
underground non-enveloped tanks in permafrost soil
for disposal of drilling waste. Permafrost is typically
a negative impact on economic development, but in
this situation it is the determining factor for a
positive role, enabling lower costs to ensure
ecological safety and, consequently, improve the
competitiveness of domestic enterprises in the
global gas market. This article is devoted to methods
of dumping drilling waste and the problems that
arise in their burial place. We discuss various
methods of waste disposal, their advantages and disadvantages, as well as the impact on the
environment
According to measurement theory, statistical data
are measured in various scales. The most widely
used ordinal scale, scales of intervals and relations.
Statistical methods of data analysis should
correspond to the scales in which the data is
measured. The term "correspondence" is specified
with the help of the concepts of an adequate
function and an allowable scale transformation. The
main content of the article is a description of the
average values that can be used to analyze data
measured in the ordinal scale, interval and
relationship scales, and some others. The main
attention is paid to the means for Cauchy and the
means for Kolmogorov. In addition to the mean,
from this point of view, polynomials and correlation
indices are also analyzed. Detailed mathematical
proofs of characterization theorems are given for the
first time in scientific periodicals. It is shown that in
the ordinal scale there are exactly n average values,
that can be used, namely, n order statistics. The
proof is represented as a chain of 9 lemmas. In the
scale of intervals from all Kolmogorov means, only
the arithmetic mean can be used. In the scale of
relations from all the Kolmogorov means, only the
power means and the geometric mean are
permissible. The kind of adequate polynomials in
the relationship scale is indicated
At the Department of "Economics and organization
of production" at the end of XX - beginning of XXI
centuries created the scientific school in the field of
organizational and economic modeling,
econometrics and statistics. The same name section
of the department oversees the teaching of the
relevant disciplines. The Laboratory of economic
and mathematical methods in controlling of the
Research and Education Center "Controlling and
innovation in management" of Bauman Moscow
State Technical University conducts research in this
domain. This article is devoted to the activities of
the scientific school, conducting research, and some
of the results. We start with a discussion of the
definitions of terms, which we use. Organizationaleconomic
modeling - scientific, practical and
academic discipline which devoted to the
development, research and application of
mathematical and statistical methods and models in
economics and management of the national
economy, especially in economics and management
of industrial enterprises and their associations. The
term "economic-mathematical methods and models"
has close content. Statistical methods in economics -
the subject of econometrics, the base of which is
applied statistics. Organizational-economic
modeling and econometrics are discussed as a
theoretical and practical trainings and discipline. We
developed textbooks and manuals on the
organizational and economic modeling,
econometrics and statistics. We have conducted
theoretical research and development of applications
in the field of organizational and economic
modeling. In particular, the prediction is regarded as
one of the management functions in industry. We
study the problem of stability in the models and
methods of development of strategy of the enterprise. For prospective organizational and
economic mechanisms of management of industrial
and economic activities, we proposed design based
on solidary information economy