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Ratio‐consistency of some invariant U‐statistic‐based estimators with an application to high‐dimensional data ranking

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  • Jia Guo
  • Bu Zhou

Abstract

Ratio‐consistency is a very desirable property of estimators, especially in high‐dimensional statistics. In this article, unbiased and rotation‐translation‐invariant estimators based on linear combinations of U‐statistics for some functions of the covariance matrix are derived using a general procedure. A useful result for showing the ratio‐consistency of such a kind of estimators utilizing the formula for the variance of U‐statistics is provided, and sufficient conditions for the ratio‐consistency of these proposed unbiased estimators are then deduced. As an application, a novel procedure using these invariant estimators to rank high‐dimensional data is proposed.

Suggested Citation

  • Jia Guo & Bu Zhou, 2025. "Ratio‐consistency of some invariant U‐statistic‐based estimators with an application to high‐dimensional data ranking," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 52(2), pages 1092-1110, June.
    • Handle: RePEc:bla:scjsta:v:52:y:2025:i:2:p:1092-1110
    DOI: 10.1111/sjos.12781
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