Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Abstract

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.

Keywords:

• EM-algorithm
• Grubbs model
• Local influence
• Skew-normal

Mathematics Subject Classification:

• 62JXX
• 62J20

Acknowledgments

The authors acknowledge two referees for their insightful comments and suggestions and partial financial support from CNPQ/FAPESP/FAPEMIG, Brasil.