On estimation and influence diagnostics for the Grubbs’ model under heavy-tailed distributions

The Grubbs’ measurement model is frequently used to compare several measuring devices. It is common to assume that the random terms have a normal distribution. However, such assumption makes the inference vulnerable to outlying observations, whereas scale mixtures of normal distributions have been an interesting alternative to produce robust estimates, keeping the elegancy and simplicity of the maximum likelihood theory. The aim of this paper is to develop an EM-type algorithm for the parameter estimation, and to use the local influence method to assess the robustness aspects of these parameter estimates under some usual perturbation schemes. In order to identify outliers and to criticize the model building we use the local influence procedure in a study to compare the precision of several thermocouples.