Asymptotic Expansions for the Distributions of Maximum and Sum of Quasi-Independent Hotelling's T² Statistics Under Non Normality

Abstract

This article presents asymptotic expansions for the joint characteristic function and the joint distribution of correlated but asymptotically independent (i.e., quasi-independent) Hotelling's T² statistics under nonnormality, which is an extension of Fujikoshi and Seo (1999) under normality. The derivation is based on the differential operator developed by Kakizawa and Iwashita (2005a). Also, asymptotic expansions for the distributions of maximum and sum of quasi-independent Hotelling's T² statistics are derived in order to construct simultaneous confidence intervals of mean vectors in the one-way layout model.

Keywords:

• Asymptotic expansion
• Differential operator
• Nonnormality
• Quasi-independent Hotelling's T ² statistics
• Simultaneous confidence intervals

Mathematics Subject Classification:

• Primary 62J15, 62H10
• Secondary 62E20, 62J10