Applied Mathematics and Control Sciences

The work is devoted to the theory of robust parameter estimation of statistical models using the apparatus of information theory. The approach of A.M. Shurygin based on the model of a series of samples with random point contamination (point Bayesian contamination model) is considered. The first part of our work describes a non-parametric method of selecting the contamination point distribution – by maximizing Shannon entropy or cross entropy in the neighborhood of the model distribution limited by the value of Kulbak – Leibler divergence. This way of finding the distribution density of the contamination point allows us to consider the resulting estimators as robust, and, moreover, having the optimality property. We call the obtained estimators generalized radical, since their special case is the radical estimators of A.M. Shurygin.In the second part of the work, another optimal solution is obtained on the basis of the formalism of A. Rényi (or the formalism of C. Tsallis equivalent in terms of our problem) that gives a new family of estimators, the special cases of which are also some well-known estimators. To select one estimate from a family defined by different divergence constraints, an optimization approach is proposed. The main theoretical results obtained in the paper are illustrated by the example of location estimating for the cosine distribution.

The main objective of factor analysis is to identify implicit factors that explain the relationships between observed variables. This makes it possible to obtain a more complete and accurate picture of the phenomena and processes being studied, which allows us to establish hidden patterns and trends that are not always possible to determine with visual data analysis. These hidden variables can be used to simplify the data and understand the main mechanisms underlying the phenomenon being studied.A quantitative assessment of the influence of each variable on the result using mathematical methods can be performed using various approaches and tools. A brief overview of the main tools is given. The choice of a specific method depends on the nature of the data, the objectives of the study and the available resources.It is known that the main disadvantage of factor analysis is the failure to fulfill the commutative (communicative) law of multiplication, which is explained by the occurrence of an indecomposable remainder. The indecomposable remainder is explained by the fact that the model under consideration does not fully take into account all the factors influencing the phenomenon under study, and therefore the variation of the feature will not be determined only by the factors under consideration, that is, some part will remain undistributed between the independent variables. Consequently, the degree of influence of a specific feature on the dynamics of the resulting component will depend on its location in the model. It is clear that with an increase in the model dimension, the number of equivalent calculation options will also increase due to an increase in the number of possible alternative versions of the solution. It should be noted that this leads to a variety of possible forms of solving the original problem, and the definition of a specific solution method will be determined by the purpose and objectives of the study. It should be noted that the number of options for the possible permutations of factors under consideration can be reduced by aggregating some factors. It is only important to clearly justify the economic meaning of such an aggregated indicator. This circumstance makes it possible to construct a procedure that allows estimating the indecomposable remainder. The article discusses a methodology for estimating the indecomposable remainder. The value of the indecomposable remainder can be defined as the difference between the data obtained in two calculation forms, between the values of the indicator in the multiplicative model, where this indicator is in last place, and in another calculation method, where the same factor is put in first place. It is shown that in the course of factor analysis there is an invariant constant that does not depend on the calculation method. Methods for reducing the dimensionality of the original problem by aggregating the original factors are also given. It is only important to clearly substantiate the economic meaning of such an aggregated indicator. The article provides an example of a three-factor model of labor productivity, when the result indicator will be determined by three factors: capital productivity, mechanical equipment of workers and the share of workers in the total number of employees of the enterprise. By combining the first two factors into one, the problem was reduced to a two-factor model of labor productivity, depending on two factors: the average output of workers and the share of workers in the total number of employees of the enterprise.

This article presents a comparative analysis of methods of constructing statistical models based on robust regression, ridge regression, kernel-based orthogonal projections to latent structures (K-OPLS), alternating conditional expectations (ACE) and direct distribution neural networks. These models are used for estimating the values of the points of fractional composition of the kerosene fraction, the product of the fractionation column. During the construction of models, the issue of meaning the values of input variables over a certain period was considered to link them to the values of output variables. Unlike the existing works, in this article, training and testing of models is carried out on segments of the data array limited in the values of the output variable. The training segment is formed from the general array by excluding observations whose values are limited by upper and lower limits. The excluded observations constitute the test sample. This paper shows the influence of the width of the interval of meaning the values of the input variable on the estimating accuracy of the resulting models. It is also shown that the lowest value of the mean absolute error for estimating the points of fractional composition is provided by models based on neural networks and K-OPLS for various training and testing options.

The article presents an analysis of various demand forecasting methods for the telecommunications company "Tricolor", using both the statistical SARIMA model and modern approaches, including XGBoost and recurrent neural networks. The study encompasses the application of these methods to assess future changes in demand for tariff plans, considering seasonal fluctuations and other influencing factors. The article addresses issues related to model tuning, parameter selection, as well as challenges and solutions associated with each method to enhance forecast accuracy. It emphasizes the significance of integrating diverse forecasting methods into strategic planning and operational management of the company in a competitive market environment and variable consumer preferences. The results can be used to form flexible demand management strategies and optimize the company's offerings.

The paper is devoted to the use of mathematical modeling methods to develop a methodological approach to assessing the effectiveness of organizations whose activities are related to innovative development. The peculiarity of innovative development is revealed and the role of organizations involved in the scientific and technological policy of the state is determined. As a result of the analysis, the main types of innovation infrastructure organizations, their functional purpose and support from the executive authorities are displayed. The theoretical part of the study is the formation of a consolidated list of performance indicators of innovation infrastructure organizations for further use in the practical component of the work. Based on the previously conducted research, the choice of mathematical tools for the development of assessment methodology is justified, which provides for the use of the theory of fuzzy sets and fuzzy logic, the method of hierarchy analysis, time series analysis. The listed set of modeling methods is applied from the point of view of the complexity of the research object: quantitative and qualitative indicators are taken into account, the involved variables are prioritized, the analyzed external factors of influence are taken into account. This approach makes it possible to increase the objectivity of the assessment results. As an example, the proposed methodological approach is used to assess one of the elements of innovation infrastructure. The conclusion emphasizes the need for a comprehensive assessment and clarifies the practical applicability of the proposed approach. The methodology can be used by public authorities for the expedient allocation of financial resources and other incentives for innovation infrastructure organizations. The methodology is also applicable for internal audit of the activities of the elements considered in this paper in order to develop recommendations to improve their own efficiency.