Consistency of the objective general index in high-dimensional settings
研究了高维条件下客观综合指数作为总体估计量的一致性，证明在维度与样本量比值趋于零时成立，并基于大偏差理论评估了正态样本的尾部概率，数值实验和实际数据应用支持了理论结果。
The objective general index is a scale-invariant weighting method for ranking of multivariate data. We show that the sample objective general index is a consistent estimator of the population counterpart in high-dimensional settings under p/n→0 together with a set of conditions, where p and n denote the dimension and the sample size. The proof is based on a recent result on random matrix theory. We also evaluate the tail probability of the estimator for normal samples based on the large deviation theory. Numerical experiments are conducted to support the theoretical result. An example of real data analysis suggests an application of the weight to variable selection.