The limiting distribution of the F-statistic from nonnormal universes

Gueven B.

STATISTICS, vol.40, no.6, pp.545-557, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 6
  • Publication Date: 2006
  • Doi Number: 10.1080/02331880601012843
  • Journal Name: STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.545-557
  • Middle East Technical University Affiliated: No

Abstract

We consider a linear regression model with an unbalanced 1-fold nested error structure, where group effect and error are from nonnormal universes. The limiting distribution of the F-statistic in this model is derived, as the sample size is large and group sizes take values from a finite set of distinct integers. The result is used to approximate the F-distribution quantile and to test the significance of the random effect variance component. Results are also applicable to the F-statistic in the one-way random-effects model. The effects of departure from normality on the F-statistic distribution are given.