Non-normal analysis of variance and regression procedures based on modified maximum likelihood estimators

Abstract

<p>The assumption of normality appears prevalently in well-known statistical procedures. This may be a drawback, since it is very often the case that the data under study is not normally distributed. It is of interest to relax this normality assumption, and extend many commonly used statistical procedures to include non-normal situations.</p> <p>With this in mind, we have proposed non-normal Regression and Analysis of Variance schemes based on Tiku and Suresh's (1992) Modified Maximum Likelihood procedure, for a symmetric non-normal family of distributions. The results have been derived both for complete and censored samples. The resulting non-normal procedures are exactly similar in form to the classical results, and are no more difficult to implement. They are also asymptotically fully efficient. Simulation studies have shown that the new methods are extremely efficient, even for distributions far from normal, and for small samples.</p> <p>It is hoped that these new techniques present viable alternatives for data analysis when the normality assumption may not be justified.</p>