Ratio‐consistency of some invariant U‐statistic‐based estimators with an application to high‐dimensional data ranking
本文推导了基于U统计量线性组合的无偏且旋转平移不变的协方差矩阵函数估计量，证明了其比率一致性，并提出了一个利用这些估计量对高维数据进行排序的新方法。
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.