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Impossibility Results for Nondifferentiable Functionals

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  • Keisuke Hirano
  • Jack R. Porter

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 continuously differentiable in the parameters of the data distribution, there exist no locally asymptotically unbiased estimators and no regular estimators. This places strong limits on estimators, bias correction methods, and inference procedures.
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Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1769-1790
    DOI: ECTA8681
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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