High-dimensional inference on covariance structures via the extended cross-data-matrix methodology

TL;DR

This paper introduces the extended cross-data-matrix (ECDM) methodology for high-dimensional inference on covariance structures, providing a new test for correlation matrices with proven consistency and asymptotic properties, validated through simulations and real data.

Contribution

The paper develops the ECDM estimator for high-dimensional correlation testing, establishing its unbiasedness, consistency, and asymptotic normality, along with a practical testing procedure.

Findings

ECDM estimator is unbiased and consistent.

The test procedure has correct asymptotic size and power.

Application to microarray data demonstrates practical utility.

Abstract

In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of ECDM estimator. We also show that the ECDM estimator has the consistency property and the asymptotic normality in high-dimensional settings. We propose a test procedure by the ECDM estimator and evaluate its asymptotic size and power theoretically and numerically. We give several applications of the ECDM estimator. Finally, we demonstrate how the test procedure performs in actual data analyses by using a microarray data set.