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

2025-06-12

AI Summary

This paper addresses the signal-to-noise ratio (SNR) estimation problem in high-dimensional linear models with multivariate responses, incorporating both fixed and random effects. We extend the method of moments—previously developed for univariate responses—to the multivariate setting for the first time, and systematically develop an SNR estimation and asymptotic inference framework accommodating residual heteroskedasticity. Specifically, we propose a heteroskedasticity-robust moment estimator, rigorously establish its asymptotic normality under high-dimensional regimes, derive analytically tractable robust standard errors, and develop corresponding inferential theory based on heteroskedasticity-robust covariance estimation. Numerical experiments demonstrate that the proposed method significantly improves estimation accuracy and stability in practical applications—such as genomic heritability estimation—while maintaining theoretical rigor and computational feasibility.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• Extend SNR estimation to multivariate linear models
• Compare asymptotic distributions of new estimators
• Handle heteroskedasticity in residual variance

Innovation

• Extends method-of-moments to multivariate responses
• Compares asymptotic distributions of new estimators
• Handles residual heteroskedasticity with inference procedures