On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

Abstract

In this paper, we discuss the extension of some diagnostic procedures to multivariate measurement error models with scale mixtures of skew-normal distributions (Lachos et al., Statistics 44:541–556, 2010c). This class provides a useful generalization of normal (and skew-normal) measurement error models since the random term distributions cover symmetric, asymmetric and heavy-tailed distributions, such as skew-t, skew-slash and skew-contaminated normal, among others. Inspired by the EM algorithm proposed by Lachos et al. (Statistics 44:541–556, 2010c), we develop a local influence analysis for measurement error models, following Zhu and Lee’s (J R Stat Soc B 63:111–126, 2001) approach. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and Cook’s well-known approach can be very difficult to apply to achieve local influence measures. Some useful perturbation schemes are also discussed. In addition, a score test for assessing the homogeneity of the skewness parameter vector is presented. Finally, the methodology is exemplified through a real data set, illustrating the usefulness of the proposed methodology.