Inference and diagnostics in skew scale mixtures of normal regression models

Abstract

AbstractSkew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation-maximization (EM) algorithms for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models and we develop diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach cannot be used to obtain measures of local influence. The EM-type algorithm has been discussed with an emphasis on the skew Student-t-normal, skew slash, skew-contaminated normal and skew power-exponential distributions. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.Keywords: skew scale mixtures of normal distributionsleveragelocal influenceEM-algorithm AcknowledgementsWe thank the editor, associate editor and two referees, whose constructive comments led to a much improved presentation. Victor Lachos acknowledges support from CNPq-Brazil (Grant 305054/2011-2) and from FAPESP-Brazil (Grant 2011/17400-6).