Inferences on location parameter in multivariate skew-normal family with unknown scale parameter

Abstract

In this paper, the statistical inference on the location parameter vector is studied in the multivariate skew-normal model with unknown scale parameter and known shape parameter. Based on the distribution of the generalized Hotelling’s T² statistic, confidence regions and hypothesis tests on the location parameter, $\mathit{\mu },$ are obtained. The power function of the test is studied numerically as well. For illustration the effectiveness and applicability of our purposed methods, the traffic accident data from the National Highway Traffic Safety Administration (NHTSA) in U.S. Department of Transportation are analyzed.

Keywords:

• Confidence regions
• Generalized Hotelling’s statistic
• Hypothesis testing
• Location parameter
• Multivariate skew-normal distribution

MATHEMATICS SUBJECT CLASSIFICATION 2020:

• 62F10
• 62F25
• 62H12

Acknowledgments

The authors would like thank the editor and referees for their helpful comments and suggestions which led to the significant improvement of the paper.