Inference After Model Averaging In Linear Regression Models

This article considers the problem of inference for nested least squares averaging estimators. We study the asymptotic behavior of the Mallows model averaging estimator (MMA; Hansen, 2007) and the jackknife model averaging estimator (JMA; Hansen and Racine, 2012) under the standard asymptotics with fixed parameters setup. We find that both MMA and JMA estimators asymptotically assign zero weight to the under-fitted models, and MMA and JMA weights of just-fitted and over-fitted models are asymptotically random. Building on the asymptotic behavior of model weights, we derive the asymptotic distributions of MMA and JMA estimators and propose a simulation-based confidence interval for the least squares averaging estimator. Monte Carlo simulations show that the coverage probabilities of proposed confidence intervals achieve the nominal level.