Estimating Signal-to-Noise Ratios for Multivariate High-dimensional Linear Models

TL;DR

This paper extends the method-of-moments approach for estimating signal-to-noise ratios to multivariate high-dimensional linear models, providing asymptotic analysis and inference methods validated by numerical experiments.

Contribution

It introduces a novel framework for SNR estimation in multivariate linear models, including fixed and random effects, with extensions for heteroskedasticity and asymptotic inference.

Findings

Asymptotic distributions of estimators are established.

Method performs well in numerical simulations.

Extensions handle residual heteroskedasticity.

Abstract

Signal-to-noise ratios (SNR) play a crucial role in various statistical models, with important applications in tasks such as estimating heritability in genomics. The method-of-moments estimator is a widely used approach for estimating SNR, primarily explored in single-response settings. In this study, we extend the method-of-moments SNR estimation framework to encompass both fixed effects and random effects linear models with multivariate responses. In particular, we establish and compare the asymptotic distributions of the proposed estimators. Furthermore, we extend our approach to accommodate cases with residual heteroskedasticity and derive asymptotic inference procedures based on standard error estimation. The effectiveness of our methods is demonstrated through extensive numerical experiments.