Multiple linear regression model under nonnormality

Islam M., Tiku M.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.33, no.10, pp.2443-2467, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 10
  • Publication Date: 2004
  • Doi Number: 10.1081/sta-200031519
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2443-2467
  • Keywords: multiple linear regression, modified likelihood, robustness, outliers, M estimators, least squares, nonnormality, hypothesis testing, MAXIMUM-LIKELIHOOD, EXPERIMENTAL-DESIGN, ROBUST, SAMPLES
  • Middle East Technical University Affiliated: No

Abstract

We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.