Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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Name

Orlov Alexander Ivanovich

Scholastic degree




Academic rank

professor

Honorary rank

Organization, job position

Bauman Moscow State Technical University
   

Web site url

Email

prof-orlov@mail.ru


Articles count: 150

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200 kb

LIMIT THEOREMS FOR KERNEL DENSITY ESTIMATORS IN SPACES OF ARBITRARY NATURE

abstract 1081504021 issue 108 pp. 316 – 333 30.04.2015 ru 968
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
241 kb

LIMIT THEOREMS IN STATISTICAL CONTROL

abstract 1161602032 issue 116 pp. 457 – 478 29.02.2016 ru 802
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
201 kb

LIMIT THEORY OF NONPARAMETRIC STATISTICS

abstract 1001406011 issue 100 pp. 224 – 242 30.06.2014 ru 1029
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
234 kb

MAIN FEATURES OF THE NEW PARADIGM OF MATHEMATICAL STATISTICS

abstract 0901306013 issue 90 pp. 188 – 214 30.06.2013 ru 1335
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
279 kb

MAIN PROBLEMS OF CONTROLLING OF THE QUALITY

abstract 1111507004 issue 111 pp. 20 – 52 30.09.2015 ru 835
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
715 kb

MANAGEMENT PROBLEMS IN SMALL PRODUCTION COMPANIES AT EARLY LIFECYCLE STAGES

abstract 1181604015 issue 118 pp. 275 – 304 29.04.2016 ru 422
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)
282 kb

MATHEMATICAL METHODS IN SOCIOLOGY DURING THE LAST FORTYFIVE YEARS

abstract 1171603004 issue 117 pp. 93 – 121 31.03.2016 ru 805
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
342 kb

MATHEMATICAL METHODS OF CLASSIFICATION THEORY

abstract 0951401023 issue 95 pp. 423 – 459 30.01.2014 ru 1118
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)
256 kb

MATHEMATICAL THEORY OF RATINGS

abstract 1141510001 issue 114 pp. 1 – 26 30.12.2015 ru 1225
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
284 kb

METHODOLOGY OF CONTROL PROCESSES MODELING IN SOCIO-ECONOMIC SYSTEMS

abstract 1011407011 issue 101 pp. 166 – 196 30.09.2014 ru 1495
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
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