Large-Deviations Theory and Empirical Estimator Choice
研究大偏差背景下信息恢复与推断的准则选择问题，证明Owen的经验似然估计量具有大偏差合理性，并将两种经验估计量与两类不适定逆问题联系起来。
In this article, we consider the problem of criterion choice in information recovery and inference in a large-deviations (LD) context. Kitamura and Stutzer recognize that the Maximum Entropy Empirical Likelihood estimator can be given a LD justification (Kitamura and Stutzer, 2002 Kitamura , Y. , Stutzer , M. ( 2002 ). Connections between entropic and linear projections in asset pricing estimation . J. Econometrics 107 : 159 – 174 .[Crossref] , [Google Scholar]). We demonstrate there exists a similar LD justification for Owen's Empirical Likelihood estimator (Owen, 2001 Owen , A. B. ( 2001 ). Empirical Likelihood . New York : Chapman-Hall/CRC .[Crossref] , [Google Scholar]). We tie the two empirical estimators and related LD theorems to two basic ill-posed inverse problems α and β. We note that other estimators in this family lack an LD footing and provide an extensive discussion of the implications of these results. The appendix contains formal statements regarding relevant LD theorems.