Impossibility results for nondifferentiable functionals

Keisuke Hirano, Jack R. Porter

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1769-1790
Number of pages22
JournalEconometrica
Volume80
Issue number4
DOIs
StatePublished - Jul 1 2012

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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