INFERENCE AFTER MODEL AVERAGING IN LINEAR REGRESSION MODELS
研究了嵌套最小二乘平均估计量的推断问题，分析了Mallows和Jackknife模型平均估计量的渐近行为，并提出了基于模拟的置信区间，蒙特卡洛模拟显示其覆盖概率达到名义水平。
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.