This talk presents two complementary approaches to estimating signal-to-noise ratios (and residual variances) in high-dimensional linear models, motivated by heritability analysis. First, I show that the REML estimator remains consistent and asymptotically normal under substantial model misspecification—fixed coefficients and heteroskedastic and possibly correlated errors. Second, I extend a method-of-moments framework to multivariate responses for both fixed- and random-effects models, deriving asymptotic distributions and heteroskedasticity-robust standard-error formulas. Simulations corroborate the theory and demonstrate strong finite-sample performance.