Needs in Development of Statistical Analysis Technology

Abstract

The mathematical fundamentals of the modern methods of experimental data analysis were developed by A.N. Kolmogorov, N. Wiener, and A.Ya. Khinchin. The most widely used algorithms for processing of measuring information are created on its basis. It is recommended to use them in the case when the classical conditions are realized, i.e., the analyzed signals are stationary, they obey the normal distribution law, the correlation between the noise and useful signal is equal to zero, and the noise is white noise. For example, while using the spectral correlation and regression analysis, the theory of random processes, and the theory of pattern recognition, we assume that the classical conditions hold true. For the cases when these assumptions are acceptable one can get satisfactory results. But there is a wide class of problems where these assumptions are not acceptable and the results of solving these problems are unsatisfactory. In this case in solving a large number of important problems one gets false results, which lead to disastrous consequences that severely influence economic and social life. It is explained by the following fact. In creating traditional algorithms the specific features of forming real signals are not sufficiently taken into consideration. For this reason the application of these algorithms for solving the most important problems does not give desired results. Therefore it is a problem of great theoretical and practical importance to develop algorithms providing the robustness of calculating appropriate estimates so that their properties remain satisfactory even if the classical conditions are violated considerably