Multivariate measurement error models based on scale mixtures of the skew–normal distribution

Abstract

Scale mixtures of the skew–normal (SMSN) distribution is a class of asymmetric thick–tailed distributions that includes the skew–normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation–maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew–t, skew–slash and skew–contaminated normal distributions. The results and methods are applied to a real data set.