ASYMPTOTIC EXPANSION FOR SAMPLING DISTRIBUTION AND SAMPLE SIZE IN STATISTICAL INFERENCE II

PROBABILITY OF MISDISCRIMINATION IN THE DISCRIMINANT ANALYSIS

Abstract

This is a follow-up paper on the subject stated in the title, the first paper [M. Siotani, T. Iwashita and T. Seo (1998)] having presented the problem by using Hotelling's T²-test. According to the idea described in the first paper, the probability of misdiscrimination (PMD) in the discriminant analysis for two groups is treated in this paper, and an experimental formula of approximate upper bound on the absolute error of the asymptotic expansion formula for PMD is constructed. An effective domain of parameters involved in the formula is determined in advance of the construction of the bound. Based on the experimental upper bound, the relationship between the accuracy of the asymptotic expansion formula and sample sizes is discussed, and a useful rule for determining a suitable sample size for which some specified requirements on PMD are satisfied is provided.