An asymptotic expansion for the distribution of the linear discriminant function based on monotone missing data

Abstract

In this study, we derive an asymptotic expansion for the distribution of a linear discriminant function based on monotone missing training data. Asymptotic expansions play an important role in discriminant analysis in that they consider the probabilities of misclassification. We derive an asymptotic expansion for linear discrimination that is based on monotone missing training data. In other words, we derive a specific generalization of the results derived by Okamoto [An asymptotic expansion for the distribution of the linear discriminant function, Ann. Math. Statist. 34 (1963), pp. 1286–1301]. Finally, we evaluate the accuracy of our result by the Monte Carlo simulation.

Keywords:

• discriminant analysis
• asymptotic expansion
• probabilities of misclassification
• asymptotic approximation
• monotone missing data

AMS Subject Classifications:

• 62H30
• 62H10

Acknowledgements

The author is indebted to Professor Takashi Seo of Tokyo University of Science for his useful comments. The author expresses his gratitude to the referees for their many invaluable comments and suggestions, which greatly enhanced the paper. Finally, the author thanks the Editor, Coordinator-Editor, and Guest Editors for providing an opportunity to be a part of a special issue devoted to LinStat’2010. This study was supported by Grant-in-Aid for JSPS Fellows (23 · 6926).

Notes

^†Research Fellow of the Japan Society for the Promotion of Science.