On Estimation and Local Influence Analysis for Measurement Errors Models under Heavy-tailed Distributions

Scale mixtures of normal distribution is a class of symmetric thick--tailed distributions that includes the normal one as a special case. In this paper we consider local influence analysis for measurement error model (MEM) when the random error and the unobserved value of the covariates follows jointly a scale mixtures of normal distribution, providing an appealing robust alternative to the usual Gaussian process in measurement error models. As the observed data log-likelihood associated with this model is intractable, Cook's well--known approach may be hard to be applied to obtain measures of local influence. Instead we develop local influence measures following the approach of Zhu and Lee (2001), which is based on the use of an EM-type algorithm. Three specific perturbation schemes are discussed. Results obtained from a real data set are reported, illustrating the usefulness of the proposed methodology.