Local False Sign Rate and the Role of Prior Covariance Rank in Multivariate Empirical Bayes Multiple Testing

TL;DR

This paper explores how the rank of prior covariance matrices affects the local false sign rate in multivariate empirical Bayes testing, revealing that low-rank matrices inflate false sign rates and proposing an adjustment to improve accuracy.

Contribution

It identifies the impact of prior covariance rank on false sign rate inflation and introduces a full-rank covariance adjustment to enhance empirical Bayes testing accuracy.

Findings

Low-rank covariance matrices inflate false sign rates.

Full-rank covariance adjustment reduces false sign rate inflation.

Simulation results confirm improved robustness in high-dimensional testing.

Abstract

This paper investigates the relationship between the rank of the prior covariance matrix and the local false sign rate (lfsr) in multivariate empirical Bayes multiple testing, specifically within the context of normal mean models. We demonstrate that using low-rank covariance matrices for the prior results in inflated false sign rates, a consequence of rank deficiency. To address this, we propose an adjustment that mitigates this inflation by employing full-rank covariance matrices. Through simulations, we validate the effectiveness of this adjustment in controlling false sign rates, thereby improving the robustness of empirical Bayes methods in high-dimensional settings. Our results show that the rank of the prior covariance matrix directly influences the accuracy of sign estimation and the performance of the lfsr, with significant implications for large-scale hypothesis testing in statistics and genomics.