This paper examines the high dimensional   asymptotics of the naive Hotelling         statistic.   Naive Bayes has been utilized in high dimensional pattern recognition as a   method to avoid singularities in the estimated covariance matrix. Though the   naive Hotelling         statistic is a   statistically important quantity in naive Bayes, its high dimensional   behavior has not been studied. In this paper, asymptotic normality of the   naive Hotelling         statistic under   a high dimension low sample size setting is developed by using the central limit   theorem of a martingale difference sequence. Simulation results under several   covariance structures are also reported.