On the Distributions of some Test Statistics for Profile Analysis in Elliptical Populations

SYNOPTIC ABSTRACT

The upper percentiles for the distributions of the test statistics in profile analysis are discussed. These test statistics are Hotelling's T²-type statistic in normal populations and their upper percentiles are expressed by that of the F-distributions. In elliptical populations, however, it is difficult to express them exactly. Then asymptotic expansions for the distributions of the test statistics are derived by the perturbation method and we obtain approximate upper percentiles for the distributions of the test statistics. The effect of nonnormality on approximations is discussed and the approximate accuracy is evaluated via a Monte Carlo simulation study.

Key Words and Phrases:

• asymptotic expansion
• Hotelling's T²-statistic
• non-normality
• Monte Carlo simulation