The University of Montana
Department of Mathematical Sciences

Technical report #11/2007

A note on the null distributions of some test statistics for profile analysis under general conditions

Solomon W. Harrar* and Jin Xu†
*Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA, Email:harrar@mso.umt.edu
†Department of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China, Email:jxu@stat.ecnu.edu.cn

Abstract

In this note, we present the asymptotic expansions of the null distributions of some test statistics for k-sample profile analysis under general conditions. It extentsMaruyama (2007, Asmptotic expansions of the null distributions of some test statistics for profile analysis in general conditions. J. Statist. Plann. Inference, 137, 506-526)’s result of two-sample case to k-sample (k = 2) situations. Further, two new test statistics are devised for testing flatness based on the normal theory likelihood ratio criterion under two different specifications for the parameter space. The asymptotic expansions for these statistics are obtained. Our derivations are much simpler and elegant in that they are based on a transformation on some known results for one-way MANOVA and Hotelling’s T2 statistics, etc. The accuracy of the asymptotic expansions in approximating the exact null distributions of the test statistics is examined via simulation studies. An application to a real data set is illustrated.

AMS Subject Classificatios: Primary 62H10; Secondary 62E20

Keywords: Asymptotic expansion, Multivariate skewness, Multivariate kurtosis, MANOVA, Robustness

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