Tests in skew–normal regression models

Abstract

A skew-normal model is the first option to fit data with presence of skewness. It is also important not to forget the existence of small samples, which can come from experimental studies of areas such as health-related, biology, pharmacology, engineering, etc, and have as one of the most common characteristics the presence of skewness. Usual statistical tests, even those with good size and power properties, do not allow valid conclusions to be drawn when only small sample sizes are available, so it is necessary to consider some corrections of the statistical tests. Improvements to statistical tests for skew-normal models in small sample sizes have not yet been developed. This article presents a correction for the signed likelihood ratio test, a Bartlett bootstrap correction for the likelihood ratio test, and a Bartlett-type bootstrap correction for the gradient test. A Monte-Carlo simulation has been performed and allows us to conclude that the proposed corrections can significantly improve the performance of the statistical test in terms of size and power. A real data set was used to illustrate the methodology developed here from an experimental engineering study.