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

Mitsuru Tamatani and Kanta Naito

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 22, 5637-5656

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.

Date: 2019
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DOI: 10.1080/03610926.2018.1517217

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