Impossibility Results for Nondifferentiable Functionals
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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Volume (Year): 80 (2012)
Issue (Month): 4 (07)
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Charles F. Manski & John V. Pepper, 1998.
"Monotone Instrumental Variables with an Application to the Returns to Schooling,"
NBER Technical Working Papers
0224, National Bureau of Economic Research, Inc.
- 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.
- Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables: With an Application to the Returns to Schooling," Virginia Economics Online Papers 308, University of Virginia, Department of Economics.
- Rosen, Adam M., 2008.
"Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities,"
Journal of Econometrics,
Elsevier, vol. 146(1), pages 107-117, September.
- Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
- Tetenov, Aleksey, 2012.
"Statistical treatment choice based on asymmetric minimax regret criteria,"
Journal of Econometrics,
Elsevier, vol. 166(1), pages 157-165.
- Aleksey Tetenov, 2009. "Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria," Carlo Alberto Notebooks 119, Collegio Carlo Alberto.
- Hirano, Keisuke & Porter, Jack, 2006.
"Asymptotics for statistical treatment rules,"
1173, University Library of Munich, Germany.
- Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
- Charles F. Manski, 2004.
"Statistical Treatment Rules for Heterogeneous Populations,"
Econometric Society, vol. 72(4), pages 1221-1246, 07.
- Charles F. Manski, 2003. "Statistical treatment rules for heterogeneous populations," CeMMAP working papers CWP03/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Dehejia, Rajeev H., 2005.
"Program evaluation as a decision problem,"
Journal of Econometrics,
Elsevier, vol. 125(1-2), pages 141-173.
- Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
- Kreider, Brent & Pepper, John V., 2003.
"Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors,"
Staff General Research Papers Archive
10229, Iowa State University, Department of Economics.
- 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.
- Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
- Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
- 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.
- Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
- Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
- 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.
- Jorg Stoye, 2009.
"More on Confidence Intervals for Partially Identified Parameters,"
Econometric Society, vol. 77(4), pages 1299-1315, 07.
- Jörg Stoye, 2008. "More on confidence intervals for partially identified parameters," CeMMAP working papers CWP11/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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