Impossibility Results for Nondifferentiable Functionals

• 成果类型: Article
• 署名作者: Hirano, Keisuke; Porter, Jack R.
• 署名单位: University of Arizona; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA8681
• 发表日期: 2012
• 页码: 1769-1790
• 关键词: confidence-intervals; inference; parameters; sets; variables; BIAS

摘要

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or a-quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one-sided quantile unbiasedness.