Influence diagnostics for Student-t censored linear regression models

Abstract

In this paper, we extend the censored linear regression model with normal errors to Student-t errors. A simple EM-type algorithm for iteratively computing maximum-likelihood estimates of the parameters is presented. To examine the performance of the proposed model, case-deletion and local influence techniques are developed to show its robust aspect against outlying and influential observations. This is done by the analysis of the sensitivity of the EM estimates under some usual perturbation schemes in the model or data and by inspecting some proposed diagnostic graphics. The efficacy of the method is verified through the analysis of simulated data sets and modelling a real data set first analysed under normal errors. The proposed algorithm and methods are implemented in the R package CensRegMod.

Keywords:

• censored regression model
• EM algorithm
• case-deletion model
• local influence

Acknowledgements

We thank the editor, an associate editor, and two referees for their valuable comments and suggestions, which led to a substantial improvement of the paper.

Additional information

Funding

The research of V.H. Lachos was supported by Grant 305054/2011-2 from CNPq-Brazil and by Grant 2014/02938-9 from FAPESP-Brazil. The research of M.B. Massuia was supported by Grant 2011/07978-0 from FAPESP-Brazil. C.R.B. Cabral is deeply indebted to CAPES-Brazil for financial support via Project PROCAD-2007 and CNPq-Brazil via Universal Project and CT-Amazônia.