arXiv 16 May 2019 · Statistics — Methodology · publishedJournal of Business and Economic Statistics (2022) · 4 citations (OpenAlex)
arXiv:1905.06491 · PDF · DOI · OpenAlex · Extracted main text
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random variables in addition to structural parameters. Inference consists of finding confidence intervals for functions of the structural parameters. Our theory provides finite-sample lower bounds on the coverage probabilities of the confidence intervals under three sets of assumptions of increasing strength. With the moderate sample sizes found in most economics applications, the bounds become tighter as the assumptions strengthen. We discuss estimation of population parameters that the bounds depend on and contrast our methods with alternative methods for obtaining confidence intervals for partially identified parameters. The results of Monte Carlo experiments and empirical examples illustrate the usefulness of our method.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Raic (2019) A multivariate Berry-Esseen theorem with explicit constants | 0.950 | 7 | 3 | 86% |
| 2 | Blundell, Duncan, and Meghir (1998) Estimating Labor Supply Responses Using Tax Reforms | 0.811 | 4 | 2 | 100% |
| 3 | Bentkus (2003) On the dependence of the Berry–Esseen bound on dimension | 0.644 | 3 | 2 | 67% |
| 4 | Freyberger and Horowitz (2015) Identification and shape restrictions in nonparametric instrumental variables estimation | 0.644 | 2 | 2 | 100% |
| 5 | Minsker (2015) Geometric median and robust estimation in Banach spaces | 0.567 | 11 | 3 | 18% |
| 6 | Wainwright (2019) High-dimensional Statistics: A Non-Asymptotic Viewpoint | 0.511 | 3 | 2 | 33% |
| 7 | Hsu, Kakade, and Zhang (2012) A tail inequality for quadratic forms of subgaussian random vectors | 0.511 | 2 | 2 | 50% |
| 8 | Manski (2007) Identification for Prediction and Decision | 0.511 | 2 | 2 | 50% |
| 9 | Bühlmann and van de Geer (2011) Statistics for high-dimensional data: methods, theory and applications | 0.511 | 2 | 2 | 50% |
| 10 | Angrist and Evans (1998) Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size | 0.511 | 2 | 1 | 100% |
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