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Impossibility Results for Nondifferentiable Functionals

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Author Info
Hirano, Keisuke
Porter, Jack

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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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15990.

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Date of creation: 29 Jun 2009
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Handle: RePEc:pra:mprapa:15990

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Related research
Keywords: bounds analysis; moment inequality models; treatment effects; limits of experiments;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

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  1. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June. [Downloadable!] (restricted)
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  2. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February. [Downloadable!] (restricted)
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  3. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
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  4. S. A. Murphy, 2003. "Optimal dynamic treatment regimes," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 331-355. [Downloadable!] (restricted)
  5. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173. [Downloadable!] (restricted)
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  6. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, 07. [Downloadable!] (restricted)
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