On uniform asymptotic risk of averaging GMM estimators

• 成果类型: Article
• 署名作者: Cheng, Xu; Liao, Zhipeng; Shi, Ruoyao
• 署名单位: University of Pennsylvania; University of California System; University of California Los Angeles; University of California System; University of California Riverside
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE711
• 发表日期: 2019
• 页码: 931-979
• 关键词: Asymptotic risk; finite-sample risk; generalized shrinkage estimator; gmm; misspecification; model averaging; nonstandard estimator; uniform approximation; C13; C36; C52

摘要

This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite-sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non-Gaussian semiparametric nonlinear models.