Professor Kanta Naito
This paper examines the high dimensional asymptotics of the naive Hotelling $T^2$ 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 $T^2$ statistic, which is equivalent to the estimator of the naive canonical correlation, 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 $T^2$ 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. (This work is a collaboration with Mitsuru Tamatani in Doshisha University.) The talk is followed by wine and finger food with the speaker in the staff room. All attendees are welcome!