Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions

Grubbs’s model (Grubbs, Encycl Stat Sci 3:42–549, 1983 ) is used for comparing several measuring devices, and it is common to assume that the random terms have a normal (or symmetric) distribution. In this paper, we discuss the extension of this model to the class of scale mixtures of skew-normal distributions. Our results provide a useful generalization of the symmetric Grubbs’s model (Osorio et al., Comput Stat Data Anal, 53:1249–1263, 2009 ) and the asymmetric skew-normal model (Montenegro et al., Stat Pap 51:701–715, 2010 ). We discuss the EM algorithm for parameter estimation and the local influence method (Cook, J Royal Stat Soc Ser B, 48:133–169, 1986 ) for assessing the robustness of these parameter estimates under some usual perturbation schemes. The results and methods developed in this paper are illustrated with a numerical example.