Nonnormal regression. I. Skew distributions


Islam M., Tiku M., Yildirim F.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.30, no.6, pp.993-1020, 2001 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 6
  • Publication Date: 2001
  • Doi Number: 10.1081/sta-100104347
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.993-1020
  • Keywords: robustness, maximum likelihood, modified maximum likelihood, least squares, Weibull, generalised logistic, MAXIMUM-LIKELIHOOD, PARAMETERS

Abstract

In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we derive modified likelihood estimators which have explicit algebraic forms and are, therefore, easy to compute. We show that these estimators are remarkably efficient, and robust. We develop hypothesis testing procedures and give a real life example.