Short Communications

Some problems of statistics of distribution mixtures with variable concentrations

R. E. Maĭboroda

National Taras Shevchenko University of Kyiv

Abstract: Some problems of estimating characteristics of random variables are considered. The observations used as a basis are a sample from a mixture of distributions, and the concentrations of components vary in the process of measurement. The distributions of components of the mixture are evaluated nonparametrically, while estimates for some functions of concentrations are both parametric and nonparametric. The estimates considered are proved to be consistent. Estimates are constructed on the basis of inhomogeneous empirical distribution functions.

Keywords: splitting of mixtures, nonparametric regression, empirical distribution functions, estimate of change-point.

Received: 20.07.1990

 English version: Theory of Probability and its Applications, 1994, 39:4, 703–707

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