Статистический анализ моделей с переменной структурой
Classification problems for univariate and multivariate observations are often encountered in statistics and economics. However, all existing approaches to solving these problems have several essential drawbacks:
1. All these methods cannot help in testing the null hypothesis of no different classes;
2. The number of classes is assumed to be known a priori;
3. Theoretical justification of performance effectiveness of these methods is lacking.
In this paper a new nonparametric method is proposed which can help us to solve these problems. This method enables us to construct consistent estimate of an unknown number of classes and to test the null hypothesis of no different classes. Besides theoretical findings, we present results of experimental analysis of this method including comparison of its characteristics with the maximum likelihood method and k-means method in different situations.