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Normalizing transformation of Dempster type statistic in high-dimensional settings

Author

Listed:
  • Masashi Hyodo
  • Hiroki Watanabe
  • Shigekazu Nakagawa
  • Tomoyuki Nakagawa

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.

Suggested Citation

  • Masashi Hyodo & Hiroki Watanabe & Shigekazu Nakagawa & Tomoyuki Nakagawa, 2023. "Normalizing transformation of Dempster type statistic in high-dimensional settings," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(22), pages 8096-8113, November.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:22:p:8096-8113
    DOI: 10.1080/03610926.2022.2056749
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