The limiting distribution of the F-statistic from nonnormal universes

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.

Keywords:

• 1-fold nested-error model
• Asymptotic normality
• F-statistic
• Idempotent matrix

Acknowledgements

The author thanks the referees for their helpful comments and suggestions.

Additional information

Notes on contributors

Bilgehan Güven

Email: [email protected]