Impossibility Results for Nondifferentiable Functionals
研究了当目标对象是数据分布的不可微泛函时，估计和推断面临的挑战，证明不存在局部渐近无偏或α分位数无偏的估计序列，为评估估计量和推断程序提供了新视角。
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 α-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.