Asymptotic Expansion of the Distribution of the Studentized Linear Discriminant Function Based on Two-Step Monotone Missing Samples

Abstract

This article proposes an asymptotic expansion for the Studentized linear discriminant function using two-step monotone missing samples under multivariate normality. The asymptotic expansions related to discriminant function have been obtained for complete data under multivariate normality. The result derived by Anderson (1973) plays an important role in deciding the cut-off point that controls the probabilities of misclassification. This article provides an extension of the result derived by Anderson (1973) in the case of two-step monotone missing samples under multivariate normality. Finally, numerical evaluations by Monte Carlo simulations were also presented.

Keywords:

• Asymptotic approximation
• Asymptotic expansion
• Linear discriminant analysis
• Monotone missing samples
• Probabilities of misclassification

Mathematics Subject Classification:

• 62H30
• 62H10

Acknowledgments

The authors are greatly indebted to Professor Toshiya Iwashita of Tokyo University of Science and Professor Naoya Okamoto of Tokyo Seiei College for their valuable comments. The authors would also like to express their sincere gratitude to the referee for his helpful comments and suggestions which enhanced this article.