Variable selection in finite mixture of location and mean regression models using skew-normal distribution

Abstract

In this article, a variable selection method for the finite mixture of location regression (FMLR) and the finite mixture of mean regression (FMMR) models with a skew-normal error are discussed. The univariate skew-normal distribution was introduced by Sahu et al. will be used in this work, which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini one and, moreover, it allows easy implementation of the EM algorithm. A penalized likelihood approach for variable selection in FMLR and FMMR models was introduced in this article. With a data-adaptive method for selecting tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection, the oracle property in estimation. The EM algorithm facilitated by Gauss–Newton method for efficient numerical computations are developed. Simulation studies and a real data set are used to illustrate the proposed methodologies.