High dimensional asymptotics for the naive Hotelling T2 statistic in pattern recognition

Abstract

Abstract This paper examines the high dimensional asymptotics of the naive Hotelling T2 statistic. Naive Bayes has been utilized in high dimensional pattern recognition as a method to avoid singularities in the estimated covariance matrix. The naive Hotelling T2 statistic, which is equivalent to the estimator of the naive canonical correlation, is a statistically important quantity in naive Bayes and its high dimensional behavior has been studied under several conditions. In this paper, asymptotic normality of the naive Hotelling T2 statistic under a high dimension low sample size setting is developed using the central limit theorem of a martingale difference sequence.