Consistency of the objective general index in high-dimensional settings

Takuma Bando, Tomonari Sei and Kazuyoshi Yata

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: 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.

Keywords: Diagonal scaling; General index; High-dimensional data; Principal component; Random matrix; Ranking (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104938

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