On the consistency of the grid method estimators for parameters of the scale mixtures of normal distributions

A. L. Nazarov

M. V. Lomonosov Moscow State University

Abstract: It is shown that in some cases, the grid maximum likelihood method estimators in the Gaussian mixture decomposition problems are consistent. Sufficient consistency conditions describing the algorithm of the concordant change of the structure of parametric set (grid mesh) and the sample size are presented.

Keywords: mixture of normal distributions; grid method for separation of mixtures; consistency; Kullback–Leibler distance; Skorokhod space.