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 tr...

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Vydáno v:	Econometrica Ročník 80; číslo 4; s. 1769 - 1790
Hlavní autoři:	Hirano, Keisuke, Porter, Jack R.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford, UK Econometric Society 01.07.2012 Blackwell Publishing Ltd Wiley-Blackwell
Témata:	Applications Bias bias‐correction bounds Differential analysis Distribution theory Dynamic models Econometric models Econometrics Estimating techniques Estimation Estimation bias Estimators Exact sciences and technology Functional analysis Global analysis, analysis on manifolds Induced substructures Inequality Inference Insurance, economics, finance Local asymptotics Mathematical independent variables Mathematics Modeling moment inequality models Motivation NOTES AND COMMENTS Parameter estimation Parametric models Probability Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Sequences Statistical inference Statistical models Statistics Studies Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Unbiased estimators Working papers Statistical distribution moment inequality models Statistical moment Bias Statistical estimation bias-correction Functional Statistical method Unbiased estimation Distribution function bounds Approximation theory Econometrics Quantile Local asymptotics Biased estimation
ISSN:	0012-9682, 1468-0262
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Popis
Shrnutí:	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.
Bibliografie:	Early versions of this paper were titled “Impossibility Results for Bounds Estimation.” We are grateful to Donald Andrews, Matias Cattaneo, Gary Chamberlain, Jinyong Hahn, Bruce Hansen, Bo Honore, Guido Imbens, Karthik Kalyanaraman, Francesca Molinari, Marcelo Moreira, Ariel Pakes, Thomas Richardson, Jamie Robins, Kevin Song, two referees, the co‐editor, and numerous seminar participants for helpful comments and suggestions. We thank the National Science Foundation for research support under Grants SES‐0962488 (Hirano), SES‐0962422 (Porter), and SES‐0438123 (Porter). SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0012-9682 1468-0262
DOI:	10.3982/ECTA8681