Normalizing transformation of Dempster type statistic in high-dimensional settings

Masashi Hyodo, Hiroki Watanabe, Shigekazu Nakagawa and Tomoyuki Nakagawa

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 22, 8096-8113

Abstract: This paper proposes a normalizing transformation of the Dempster statistic for testing the equality of two mean vectors with unequal covariance matrices in high-dimensional settings. The distribution of the Dempster statistic is known to converge to a normal distribution as dimension p goes to infinity; however, its rate of convergence is not guaranteed. Therefore, normal approximation is often too loose for medium p settings or fails to capture the tail behavior of the resulting distribution. We developed a concept of normalizing transformation of a statistic based on the rate of convergence to normality and show that the rate of convergence to normality is improved by normalizing transformation of the Dempster statistic.

Date: 2023
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DOI: 10.1080/03610926.2022.2056749

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