Математико-статистичні методи у моніторингових економетричних дослідженнях

Abstract

Quality monitoring in modern conditions is carried out using mathematical and statistical methods. With the help of mathematical and statistical methods of research, large amounts of information are processed and causal dependencies are established. The use of statistical techniques contributes to the ability to read reports on statistical studies in the field of education and economics, and teaches techniques for analyzing the data obtained. The article uses a method of multidimensional statistical analysis, defines the identification of the mathematical-statistical model and calculates the coefficients of the influence of the model parameters on the required values of the economic characteristics of a complex system . The main tool for processing incoming information is the theory of random matrices. The construction of mathematical models in modern conditions in the application of a very large number of parameters requires the development of such approaches, which can take into account all the necessary situations, without losing important input information. The development of statistical methods often requires obtaining objective information to select a method for forecasting and assessing the situation. The task is to show the advantages of using some probabilistic approaches in the examples of a complex economic system (assessing the quality of education). Analysis of recent research and publications. Theoretical-probabilistic approach to the solution of applied problems, in which the number of parameters is large, was considered in the works of V.L. Girko [1-4]. The constructed apparatus in the theory of random matrices is tested on dimensionless input data and the research was conducted on examples of complex mathematical models. The aim of the study. There is a lot of applied tasks in the life of a society in which it is almost impossible to calculate the set of indicators without using the construction of models. Assessment of the quality of education and forecasting is an urgent task for which the scientific method of mathematical statistics must be applied. However, looking at the data, it becomes clear that they have time and space restrictions. The multidimensionality of economic and technical indicators of each unit enhances the intuitive assessment of the situation in each case. Many tests are unprofitable, and the characteristics of the parameters come with disabilities. It becomes clear that the use of multivariate statistical analysis allows you to take into account all these complexities. It is proposed to perform a statistical processing of a large number of observations, taking into account probable errors within the constraints assumed. To more accurately identify the proposed mathematical-statistical model, it is necessary to gather all the information at different moments and write it in the corresponding matrix. This information should be taken into account constantly. Keywords : multi-statistical analysis, probability, mathematical model, stochastic matrix