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!


Professor Kanta Naito

Research Area

Shimane University, Japan


Fri, 18/03/2016 - 4:00pm to 5:00pm


RC-4082, The Red Centre, UNSW