Minimum distance estimation in a finite mixture regression model

Finite mixture models provide a mathematical basis for the statistical modeling of a wide variety of random situations, and their importance for the statistical analysis of data is well documented. This article focuses on a finite mixture regression model and develops an estimator of the parameters in the model using a minimum-distance technique. In general, minimum-distance estimators are consistent and asymptotically normal when the data come from a member of the model family. Furthermore, it has been observed that they are “automatically robust” with respect to the stability of the quantity being estimated. In this paper, we employ the Hellinger distance approach introduced by Beran (1977) [5] and construct a minimum Hellinger distance estimator for a finite mixture regression model. We study the asymptotic properties such as consistency and the asymptotic normality of the proposed estimator. The small-sample and robustness properties of the proposed estimator are also examined using a Monte Carlo study, and a computational algorithm is presented.