#### Name

Orlov Alexander Ivanovich

#### Scholastic degree

•

•

•

#### Academic rank

professor

#### Honorary rank

â€”

#### Organization, job position

Bauman Moscow State Technical University

#### Web site url

â€”

## Articles count: 150

Some estimators of the probability density function in spaces of arbitrary nature are used for various tasks in statistics of non-numerical data. Systematic exposition of the theory of such estimators had a start in our work [2]. This article is a direct continuation of the article [2]. We will regularly use references to conditions and theorems of the article [2], in which we introduced several types of nonparametric estimators of the probability density. We studied more linear estimators. In this article we consider particular cases - kernel density estimates in spaces of arbitrary nature. When estimating the density of the one-dimensional random variable, kernel estimators become the Parzen-Rosenblatt estimators. Asymptotic behavior of kernel density estimators in the general case of an arbitrary nature spaces are devoted to Theorem 1 - 8. Under different conditions we prove the consistency and asymptotic normality of kernel density estimators. We have studied uniform convergence. We have introduced the concept of "preferred rate differences" and studied nuclear density estimators based on it. We have also introduced and studied natural affinity measures which are used in the analysis of the asymptotic behavior of kernel density estimators. We have found the asymptotic behavior of dispersions of kernel density estimators and considered the examples including kernel density estimators in finite-dimensional spaces and in the space of square-integrable functions

The article analyzes the development of the theory
of statistical control (from the XVIII century to the
present). Prof. M.V. Ostrogradskii (1846) clearly
describes the practical needs (ie, arising from the
quality assurance of large quantities of bags of
flour or pieces of cloth), to meet whom he spent his
research. At the same time Simpson was among the
ideas of probability theory XVIII century.
Therefore prof. M.V. Ostrogradskii may be
regarded as the founder of the theory of statistical
process control (not only in our country but all over
the world). Limit theorems of probability theory
and mathematical statistics have provided a
number of asymptotic results in problems of
statistical quality control, offer based on these best
practices. However, we must find out how much
interest among specialists characteristics are
different from limit for finite sample sizes. Such
research for the synthesis algorithm control plan on
the basis of the limit average output level of defects
is made in this article, and for the synthesis
algorithm control plan on the basis of the
acceptance and the rejection levels of defects - not
yet (clarification of the conditions of applicability
of this algorithm - unsolved problem of applied
mathematics). We have briefly reviewed the
development of our researches on the statistical
control. Control units can be not only some units of
production, but also documents (with internal and
external audit), and standard units of air, water and
soil in the environmental monitoring. One of the
achievements can be regarded as the transfer of
statistical control of production for environmental
monitoring

We have studied the asymptotic behavior of a broad class of nonparametric statistics, which includes statistics of omega-square type and Kolmogorov-Smirnov type. Limit theorems have been proved. We have also developed the method of approximation with step functions. With the help of this method we have obtained a number of necessary and sufficient conditions

The new paradigm of mathematical statistics is based on the transition from parametric to nonparametric statistical methods, the numerical data - to non-numeric, on the intensive use of information technology. Its distinctive features are revealed in comparison with the old paradigm of mathematical statistics in the mid-twentieth century

Controlling of statistical methods to ensure product
quality is the special case of controlling
organizational and economic methods of
management. Today, controlling in the practice of
management of Russian companies is understood
as "the system of information-analytical and
methodological support to achieve their goals." The
controller is developing a decision-making rules,
the head takes decisions on the basis of these rules.
We proved the concept of "controlling of
methods". Innovation in management is based, in
particular, on the use of new adequate
organizational-economic (as well as economicmathematical
and statistical) methods. Controlling
in this area - is the development and application
procedures of compliance management used and
newly developed (implemented) organizationaleconomic
methods for the task. Thus, the
methodology for controlling is of great practical
value in any field in which the actions (operations)
must be carried out in accordance with certain rules
(regulations, standards, guidelines), as in any such
area in which we need to use development and
application procedures of compliance management
used and the newly established (implemented)
rules for solution of tasks assigned to the
organization. In this article, we select a area of
controlling as controlling quality, and we discuss
its main issues. This is about controlling of
organizational-economic methods to ensure
product quality, especially about the statistical
methods based on probability theory and
mathematical statistics. We consider the analysis
and synthesis of plans of statistical quality control,
optimization options plans of statistical control,
truncated plans. Are discussed the differences
control plans provider and the consumer, the
allocation of units formless (liquid, gas) products,
the selection of a random sample of the statistical
quality control of products, lower estimate of the
required sample size. It is established, that is not
always necessary quality control. Is given the
theory of the basic paradox of statistical quality
control. We discuss the development of statistical
methods for quality control in our country. Is given
the classification of statistical methods of quality management

In 1970 in the journal publications of "Forbes" and
"Business week" the term of "startup" appeared,
which later became popular in the scientific and
business literature. Startups are the organizations,
which create a new product or service under
conditions of high uncertainty. In the last 25-30
years, due to Russia's transition from a planned
economy to the mixed, many researchers and
practitioners in the field of management, economics
and entrepreneurship are concerned of some
questions of small business, including production. It
is particularly acute problem of deaths of Russian
small businesses: only three out of a hundred small
businesses manage to survive for more than 3 years.
In addition, one of the main reasons, why we have
such statistics, is management deficiencies and
administrative errors, which are studied in this
article. We are primarily interested in small
manufacturing plants and problems of development
in the early stages of the life cycle. In the literature,
it has been given just little attention. A small
production company is a company associated with
the production organization or incorporation of the
product / technology in the production process. We
regard the small production companies at an early
stage of development, working in the field of
mechanical engineering, instrumentation, energy,
telecommunications, robotics, materials production.
In this work, we analyze the first foreign and then
domestic research on small business, discuss the
problems of management of small industrial
enterprises in the early stages of the life cycle (based
on the results of our questionnaire studies) and as an
example, consider the story of a startup - All-Union
Center of statistical methods and Informatics of
Central Board of the All-Union economic society
(now - Institute of high statistical technologies and econometrics of Bauman Moscow State Technical
University)

Sociology is one of the most important social
sciences. Mathematical and primarily statistical
methods are effective intellectual tools of
sociologists. Let us analyze the work of the author of
this article on the development of statistical methods
to meet the challenges of sociology. Then we give
the review of development of statistical methods in
Russian sociology for 45 years (1970-2015). The
basic scientific events of these years, first of all, were
formation of applied statistics and its basis - statistics
of the non-numerical data (in sociology of 70-90% of
variables have non-numerical nature). Over the last
30 years, the Russian sociology has been growing
rapidly in all quantitative parameters. Clearly, the
depth of investigation gives the use of advanced
scientific apparatus - methodology and methods of
data collection and analysis, mathematical models. In
our view, a fundamental breakthrough was made in
our country in the 1970s. It was then in the arsenal of
Russian sociologists appeared measurement theory
and fuzzy sets, mathematical methods of
classification and multidimensional scaling,
nonparametric statistics and statistics of non-numeric
data. In subsequent decades it has been a natural
development of scientific apparatus. The same
mathematical and statistical methods and models can
be successfully applied in various fields of science
and practice. Statistical methods and models are very
effective in sociological, socio-economic,
managerial, technical and feasibility studies,
medicine, history, in almost any industry and
application areas of knowledge. Within this field, the
main event of the last thirty five years - is becoming
a scientific and practical discipline "Applied
Statistics", dedicated to the development and
application of statistical methods and models. An
analysis of the dynamics of applied statistics leads to
the conclusion that in the XXI century the statistics
of non-numerical data is becoming a central area of
applied statistics, as it contains the most common
approaches and results

This article gives a review of mathematical methods of construction and using of classifications. The main approaches to solving the problems of cluster analysis and grouping are discussed. We have also proposed global and local natural classification criteria. The methods of discriminant analysis
(diagnosis, pattern recognition with the teacher) are discussed in connection with the construction of generalized indicators (ratings)

When developing management solutions with the
aim of joint consideration and comparison of
various factors, partial removal of uncertainty is
widely used ratings. In the theory of decisionmaking
in almost the same sense, we use the terms
"composite index" or "integrated indicator". The
article is devoted to the mathematical theory of
ratings as tools for studying socio-economic
systems. We considered, primarily, linear ratings
which is a linear function from a single (private)
indicators (factors, criteria), constructed using the
coefficients of importance (weightiness,
importance). The study discusses the factors
affecting the magnitude of the ratings. Three groups
of causes affect the value of a line ranking: the ways
of measurement of individual indicators, the choice
of the set of indicators; the values of the coefficients
of importance. We considered binary ratings when
the rating takes two values. To compare the
proposed rankings we use a new indicator of the
quality of diagnostics and prognostic power.
Significantly, in many managerial situations,
significant differences between objects are identified
using any rating. According to the fundamental
results of stability theory, the same source data
should be processed in several ways. Matching
findings, obtained using multiple methods, likely
reflect the properties of reality. The difference is the
result of a subjective selection method. When using
the results of the comparison of objects according to
several indicators (criteria ratings), including in
dynamics, very useful is the selection of the Pareto
set. We discuss the examples of the application of
the decision theory, expert evaluations and rankings
when developing complex technical systems

The article introduces the basic concepts of control theory. It has also noted the multicriteriality of real control problems. After reviewing the basic concepts of the theory of modeling we have analyzed postwar history and current status of mathematical modeling of control processes. We have also discussed the modeling methodology. As an example of a real model of the management process we have considered a model of allocation of time between the acquisition of knowledge and development of skills