Misspecification Analysis of High-Dimensional Random Effects Models for Estimation of Signal-to-Noise Ratios

Estimation of signal-to-noise ratios and noise variances in high-dimensional linear models have important applications in statistical inference, hyperparameter selection, and heritability estimation in genomics. One common approach in practice is maximum likelihood estimation under random effects models. This paper aims to conduct model misspecification analysis on the consistency of this method, in which the true model only has fixed effects. Assume that the ratio between the number of samples and features converges to a nonzero constant, our results provide conditions on the design matrices under which random effects model based maximum likelihood estimation is asymptotically consistent in estimating the SNR and noise variance. Our model misspecification analysis also extends to the high-dimensional linear models with feature groups, in which group SNR estimation has important applications such as tuning parameter selection for group ridge regression.