08.00.13 Mathematical and instrumental methods of Economics

08.00.13 Mathematical and instrumental methods of Economics
DescriptionTraditionally, control decisions are made by solving repeatedly the forecasting problem for different values of control factors and choosing a combination of them that ensures the transfer of the control object to the target state. However, real control objects are affected by hundreds or thousands of control factors, each of which can have dozens of values. A complete search of all possible combinations of values of control factors leads to the need to solve the problem of forecasting tens or hundreds of thousands or even millions of times to make a single decision, and this is completely unacceptable in practice. Therefore, we need a decisionmaking method that does not require significant computing resources. Thus, there is a contradiction between the actual and the desired, a contradiction between them, which is the problem to be solved in the work. In this work, we propose a developed algorithm for decisionmaking by solving the inverse forecasting problem once (automated SWOT analysis), using the results of clusterconstructive analysis of the target states of the control object and the values of factors and a single solution of the forecasting problem. This determines the relevance of the topic. The purpose of the work is to solve the problem. By decomposing the goal, we have formulated the following tasks, which are the stages of achieving the goal: cognitivetarget structuring of the subject area; formalization of the subject area (development of classification and descriptive scales and gradations and formation of a training sample); synthesis, verification and increasing the reliability of the model of the control object; forecasting, decisionmaking and research of the control object by studying its model. The study uses the automated systemcognitive analysis and its software tools (the intelligent system called "Eidos") as a method for solving the set tasks. As a result of the work, we propose a developed decisionmaking algorithm, which is applicable in intelligent control systems. The main conclusion of the work is that the proposed approach has successfully solved the problem

TECHNOLOGY TRANSFER MODELS BETWEEN THE DEFENSE AND CIVIL SECTOR OF ECONOMY
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article considers the problem of increasing the efficiency of budget expenditures due to the transfer of military technology to the civilian sector of the economy. An analysis of foreign experience has shown that private companies are widely involved in a number of states to solve some of the infrastructure problems in the military sphere. In the USA, private companies provide communications and provide other information services to state power structures, which makes it possible to develop private business on the one hand and save budget expenses on the other. An analysis of domestic experience has shown that the use of military technologies for the production of civilian products and services in some cases can significantly save time and other resources. A model for the interaction of civilian companies with the defense complex and a diffusion model of military technologies have been developed. The article proposes creation of new structures that solve the problems of adapting military technologies to the requirements of civilian customers, as well as a database of adapted technologies and a technical investment center that supports small and mediumsized enterprises in the acquisition of equipment and technical documentation. The authors believe that the approaches proposed in the article to solving the problem of technology transfer will stimulate innovative activity in the country, reduce import dependence and increase the efficiency of budget expenditures

PROBABILITYSTATISTICAL MODELS OF CORRELATION AND REGRESSION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe correlation and determination coefficients are widely used in statistical data analysis. According to measurement theory, Pearson's linear paired correlation coefficient is applicable to variables measured on an interval scale. It cannot be used in the analysis of ordinal data. The nonparametric Spearman and Kendall rank coefficients estimate the relationship of ordinal variables. The critical value when testing the significance of the difference of the correlation coefficient from 0 depends on the sample size. Therefore, using the Chaddock Scale is incorrect. When using a passive experiment, the correlation coefficients are reasonably used for prediction, but not for control. To obtain probabilisticstatistical models intended for control, an active experiment is required. The effect of outliers on the Pearson correlation coefficient is very large. With an increase in the number of analyzed sets of predictors, the maximum of the corresponding correlation coefficients — indicators of approximation quality noticeably increases (the effect of “inflation” of the correlation coefficient). Four main regression analysis models are considered. Models of the least squares method with a determinate independent variable are distinguished. The distribution of deviations is arbitrary, however, to obtain the limit distributions of parameter estimates and regression dependences, we assume that the conditions of the central limit theorem are satisfied. The second type of model is based on a sample of random vectors. The dependence is nonparametric, the distribution of the twodimensional vector is arbitrary. The estimation of the variance of an independent variable can be discussed only in the model based on a sample of random vectors, as well as the determination coefficient as a quality criterion for the model. Time series smoothing is discussed. Methods of restoring dependencies in spaces of a general nature are considered. It is shown that the limiting distribution of the natural estimate of the dimensionality of the model is geometric, and the construction of an informative subset of features encounters the effect of "inflation coefficient correlation". Various approaches to the regression analysis of interval data are discussed. Analysis of the variety of regression analysis models leads to the conclusion that there is no single “standard model”

BASIC REQUIREMENTS FOR DATA ANALYSIS METHODS (ON THE EXAMPLE OF CLASSIFICATION TASKS)
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThere is a need to clean up the classification methods. This will increase their role in solving applied problems, in particular, in the diagnosis of materials. For this, first of all, it is necessary to develop requirements that classification methods must satisfy. The initial formulation of such requirements is the main content of this work. Mathematical classification methods are considered as part of the applied statistics methods. The natural requirements to the considered methods of data analysis and the presentation of calculation results arising from the achievements and ideas accumulated by the national probabilistic and statistical scientific school are discussed. Concrete recommendations are given on a number of issues, as well as criticism of individual errors. In particular, data analysis methods must be invariant with respect to the permissible transformations of the scales in which the data are measured, i.e. methods should be adequate in the sense of measurement theory. The basis of a specific statistical method of data analysis is always one or another probabilistic model. It should be clearly described, its premises justified  either from theoretical considerations, or experimentally. Data processing methods intended for use in realworld problems should be investigated for stability with respect to the tolerances of the initial data and model premises. The accuracy of the solutions given by the method used should be indicated. When publishing the results of statistical analysis of real data, it is necessary to indicate their accuracy (confidence intervals). As an estimate of the predictive power of the classification algorithm, it is recommended to use predictive power instead of the proportion of correct forecasts. Mathematical research methods are divided into "exploratory analysis" and "evidencebased statistics." Specific requirements for data processing methods arise in connection with their "docking" during sequential execution. The article discusses limits of applicability of probabilisticstatistical methods. Concrete statements of classification problems and typical errors when applying various methods for solving them are also considered

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn the article, we develop the methodology of strategic planning and management of the holding on the theoretical basis of automated systemcognitive analysis (ASCanalysis). This methodology provides scientific research of any holding by creating and researching its model. The methodology includes both the synthesis, adaptation and verification of systemcognitive models of the holding, and the use of these models for strategic planning and decision support for managing the holding, as a complex, multiparametric, nonlinear system. The relevance of the research is due to the special role of holdings and other corporate integrated structures both in Russia as a whole and, in particular, in the Krasnodar region. Despite obvious system advantages, holdings face a wide range of problems related to management efficiency, ensuring their sustainable functioning, etc. The proposed methodology offers ways to solve these problems and can be successfully applied in holdings and other corporate integrated structures of various regions, volumes and areas of activity, which determines the relevance of the research topic. The level of significance and scientific novelty of the Research consists in the development of conceptual and theoretical and methodological provisions aimed at managing the development of holdings. The expected results and their significance are that the methodology developed as a result of the Research can be applied by holding companies and other corporate integrated structures and will significantly improve the quality of their management

PRICING METHOD BASED ON THE ESTIMATION OF DEMAND FUNCTION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionWhen solving some problems of economics and management at an enterprise, it becomes necessary to determine the retail price of a product or service at a known wholesale price or producer price. We offer to determine the retail price based on an analysis of a survey of potential consumers about the maximum possible price for the product or service in question. We calculate the retail price on the basis of optimizing the economic effect equal to the product of the result from the sale of one unit of goods by the demand function, which we estimate by interviewing consumers. To solve the optimization problem, we approximate the demand function using the least squares method. As examples, the linear and power models of the demand function are analyzed. Ways of further development of the proposed approach are discussed. Unresolved scientific problems are formulated. Methods for estimating the demand function in the context of a large number of repetitions of respondents and their tendency to “round numbers” require further elaboration, as a result of which the Kolmogorov criterion cannot be used to determine the accuracy of the restoration of the demand function. Various parametric and nonparametric approaches of regression analysis should be adapted to the problem of restoring the dependence of demand on price, as well as methods for solving the corresponding optimization problems

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn modern economic theory, there is no complete classification of innovative approaches to the management of knowledgeintensive and hightech companies and enterprises. Among these approaches, we can highlight situational, structural, process, functional and projectbased approaches. The projectoriented approach, as a purposeful method of future systems forming, is a kind of continuation of the process approach; however, it gives priority not to the process, but to the project, as the main production, innovation and competing business unit. This article provides a brief overview of carried out research in this subject area, analyzes the advantages and opportunities of existing project management validity models, and suggests the author's approach of building a model for identifying and evaluating the potential of modern projectoriented companies and enterprises. This article also shows that the economic efficiency of such companies and enterprises achieving by using the projectbased method both in the integrated system of strategic management and in the main production activities. This leads to an increase in their ability to choose the right way of operational decisionmaking, contributes to the installation of advanced technological and technical equipment, and accelerates the commissioning of new production facilities

STRATEGIC PLANNING AND MANAGEMENT OF A HOLDING BASED ON INFORMATION AND COGNITIVE TECHNOLOGIES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn the article, we develop the methodology of strategic planning and management of a holding, on the theoretical basis of automated systemcognitive analysis (ASCanalysis). This methodology provides scientific research of any holding by creating and researching its model. The methodology includes both the synthesis, adaptation and verification of systemcognitive models of the holding, and the use of these models for strategic planning and decision support for the management of the holding, as a complex, multiparametric, nonlinear system. The relevance of the research is due to the special role of holdings and other corporate integrated structures both in Russia as a whole and, in particular, in the Krasnodar region. Despite obvious system advantages, holdings face a wide range of problems related to management efficiency, ensuring their sustainable functioning, etc. The proposed methodology offers ways to solve these problems and can be successfully applied in holdings and other corporate integrated structures of various regions, volumes and areas of activity, which determines the relevance of the research topic. The level of significance and scientific novelty of the Research consists in the development of conceptual and theoretical and methodological provisions aimed at managing the development of holdings. The expected results and their significance are that the methodology developed as a result of the Research can be applied by holding companies and other corporate integrated structures and will significantly improve the quality of their management

SYSTEM OF MODELS AND METHODS OF TESTING THE HOMOGENEITY OF TWO INDEPENDENT SAMPLES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe new paradigm of mathematical research methods allows us to give a systematic analysis of various statements of statistical analysis problems and methods for solving them, based on a probabilisticstatistical model of generating data accepted by the researcher. Methods for testing the homogeneity of two independent samples  a classic area of mathematical statistics. For more than 110 years since the publication of the fundamental Student’s article, various criteria have been developed for testing the statistical hypothesis of homogeneity in various statements, and their properties have been studied. However, the need for streamlining the totality of the scientific results found is urgent. It is necessary to analyze the whole variety of problem statements for testing the statistical hypotheses of the homogeneity of two independent samples, as well as the corresponding statistical criteria. This analysis is devoted to this article. It contains a summary of the main results concerning the methods for testing the homogeneity of two independent samples, and a comparative study of them, allowing the system to analyze the diversity of such methods in order to select the most appropriate for processing specific data. Based on the basic probabilisticstatistical model, the main statements of the problem of testing the homogeneity of two independent samples are formulated. A comparative analysis of the Student and Cramer  Welch criteria, designed to test the homogeneity of mathematical expectations, is given, a recommendation on the widespread use of the Cramer  Welch criterion is substantiated. From nonparametric methods for testing homogeneity, the criteria of Wilcoxon, Smirnov, Lehmann  Rosenblatt are considered. Dismantled two myths about the Wilcoxon criteria. Based on the analysis of the publications of the founders, the incorrectness of the term "Kolmogorov – Smirnov criterion" is shown. To verify absolute homogeneity, i.e. coincidence of the distribution functions of samples, it is recommended to use the Lehmann  Rosenblatt criterion. The current problems of the development and application of nonparametric criteria are discussed, including the difference between nominal and real significance levels, making it difficult to compare power of criteria, and the need to take into account coincidences of sample values (from the point of view of the classical theory of mathematical statistics, the probability of coincidences is 0)

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article provides a comparative analysis of assessments of the socioeconomic development of the Krasnodar region from such wellknown rating agencies as Standard & Poors, Moody’s, Fitch Ratings, which belong to the United States of America. The studied ratings are compared with the ratings of the national agency of the Russian Federation called “Expert RA”. The values of the established ratings are examined, as well as number of possible reasons why the ratings of the United States of America differ from the ratings of the Russian Federation, for example, economic and political reasons, and, subsequently, how these ratings affect the investment attractiveness of the Krasnodar region. The article explains positive and negative aspects of the integrated methodology used by international rating agencies, consisting of software and expert opinion, the level of access to it for study and analysis. We study another (local) source of information on the investment attractiveness of the Krasnodar region, which is a state institution, namely the Department of Investments and Development of Small and Medium Enterprises of the Krasnodar region. Options are proposed for improving the system of analysis of statistical data through methods that are based on a clear mathematical approach to provide an adequate assessment of the region and municipalities without the influence of subjective expert opinion