Influence Diagnostics for Censored Linear Regression Models with Skewed and Heavy-tailed Distributions

Thalita do Bem Mattos
Víctor H. Lachos
Aldo M. Garay

The scale mixtures of skew-normal (SMSN) distributions (Lachos et al., 2010) form an attractive class of asymmetrical heavy-tailed densities that includes the skew-normal, skew-t, skew-slash, skew - contaminated normal and the entire family of cale mixtures of normal (SMN) distributions as special cases. A robust censored linear model based on the scale mixtures of skew-normal (SMSN) distributions has been recently proposed by Mattos et al.(2015), where a stochastic approximation of the EM (SAEM) algorithm is presented for iteratively computing maximum likelihood estimates of the parameters. In this paper, to examine the performance of the proposed model, case-deletion and local influence techniques are de veloped to show its robust aspect against outlying and influential observations. This is done by analyzing the sensitivity of the SAEM estimates under some usual perturbation schemes in the model or data and by inspecting some proposed diagnostic graphs. The efficacy of the method is verified through the analysis of simulated datasets and modeling a real dataset from stellar astronomy previously analyzed under normal errors.

Case-deletion model
Censored regression model
Local influence
SAEM algo- rithm