Robust Multivariate Measurement Error Model with Skew-Normal/Independent Distributions

Skew-normal/independent distributions is a class of asymmetric thicktailed distributions that includes the skew-normal distribution as a especial case. The main virtue of the members of this class of distributions is that they are easy to simulate from and they make it possible to implement the Monte Carlo EM algorithm for maximum likelihood estimation. In this paper, we take skew-normal/independent distributions (Lachos and Vilca, 2007) for the unobserved value of the covariates (latent variable) and symmetric normal/independent (Lange and Sinsheimer, 1993) distributions for the random errors providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Specific distributions examined include univariate and multivariate versions of the skew-normal, the skew-t, the skew-slash and the contaminated skew-normal distribution. The results and methods are applied to a real data set.