08.00.13 Mathematical and instrumental methods of Economics

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”

INTEGRAL ASSESSMENT OF THE KRASNODAR REGION INSTITUTIONS OF HIGHER EDUCATION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article presents the results of a study of higher education institutions in the Krasnodar region based on the use of an integrated approach, identifies priority aspects of the development of universities. The level of the educational institution was calculated taking into account educational, research and international activities, staff and infrastructure. Information about the level of assessment of educational institutions is used by university applicants when they choose a particular institution. The work was carried out on the basis of monitoring the performance of educational institutions of higher education in the Krasnodar region in 2018. During the integral assessment, standardization methods were used to compare the indicator with the reference and linear transformations, as well as the method of additive convolution and the method of calculating distances. The studies showed the level of each institution of higher education, the ways of their development are highlighted. Thus, the assessment of higher education institutions, carried out on the basis of an integral indicator, covers almost all aspects of educational institutions, it allows you to quickly and objectively get an idea of universities, identify weaknesses and strengths, the results of the development of the main components of higher education institutions, and identify the reserves necessary to ensure its sustainable and effective development

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn their previous works, the authors solved the problem of cognitivetarget structuring and formalization of the subject area, as well as the synthesis and verification of statistical and systemcognitive models. This work is devoted to the application of these models to solve the problem of forecasting the impact of the volume and direction of investment in agriculture on the economic component of the quality of life of the population of the region. This work is devoted to the use of previously created and verified models to solve the problem of decisionmaking on the volume and direction of investment in agriculture, improving the quality of life of the population of the region

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThis work is devoted to revealing some opportunities of the research of a subject to modeling by a research of its model given by the ASCanalysis and the Eidos system

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article discusses the use of machine learning methods and fuzzy production systems for studying the social and economic development of urban districts, areas and settlements of the Krasnodar region. The fundamental patterns and their connection with quantitative and qualitative indicators are considered

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThis article is devoted to rating assessment of the socioeconomic situation of the Krasnodar region, presented by such agencies as "RAEKSAnalytics", "Expert RA" and "National Rating Agency". The methodologies used by these agencies were studied and analyzed. A comparison of these methodologies was also conducted. As a result, a number of their shortcomings were identified, including the lack of a complete methodological model in the public domain. Some agencies do not provide links to statistics that are used in the analysis. In the article using the STATISTICA environment, a statistical analysis of data reflecting the level of socioeconomic situation of the Krasnodar region is carried out. Based on the work [12], the article created a discriminant model for assessing the socioeconomic development of urban districts of the Krasnodar region with a confidence of 85%. The study conducted a cluster, discriminant, classification (decision trees), coefficient (proposed by the authors) based on the data of the Federal State Statistics website for the period from 2009 to 2018 in the city districts: Krasnodar, Anapa, Armavir, Gelendzhik, Goryachiy Klyuch, Novorossiysk Sochi. During the study, analyzes such as cluster and classification trees showed poor results, since they are not able to detect latent nonlinear relationships between the study indicators. Using the constructed discriminant model, we have carried out an analysis of the socioeconomic development of urban districts of the Krasnodar region for the period 20092018, which allows us to identify the leaders and the outsiders

08.00.13 Mathematical and instrumental methods of Economics
DescriptionWe use an adaptive management system for open systems to assess the impact of investments on the results of the Agroindustrial complex

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
DescriptionThe problem of the optimal distribution of production tasks is one of the important problems of effective planning of processes associated with production at the enterprise. However, the classical approach to solving this problem becomes of little use when the individual stages of the production process are performed sequentially and in the case when it is necessary to take into account the structural features of the technological processes of the enterprise. Purpose of work: to develop a methodology for minimizing costs in the distribution of production tasks, taking into account the structural features of the technological processes of the enterprise. We built a multicriteria discrete optimization model for the distribution of production tasks according to the structure of production elements. One of the methods based on the proposed model is proposed, which allows to identify groups consisting of four elements in the production structure of the enterprise. The model is built using a network design which are prefractal graphs. The use of prefractal graphs allows you to naturally represent the structure of production and technological links of the elements of the production system of large enterprises. The results of the work is the developed effective methodology for solving the problem of the network distribution of production tasks, taking into account the structural features of technological processes at the enterprise, the economic effect of which is to minimize resource costs. Based on the constructed model, we can develop automated means of monitoring and managing the production processes of a company