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Inference in a class of optimization problems: Confidence regions and finite sample bounds on errors in coverage probabilities

Joel L. Horowitz, Sokbae Lee

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

Abstract

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.

Citation extraction

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Raic (2019) A multivariate Berry-Esseen theorem with explicit constants0.9507386%
2Blundell, Duncan, and Meghir (1998) Estimating Labor Supply Responses Using Tax Reforms0.81142100%
3Bentkus (2003) On the dependence of the Berry–Esseen bound on dimension0.6443267%
4Freyberger and Horowitz (2015) Identification and shape restrictions in nonparametric instrumental variables estimation0.64422100%
5Minsker (2015) Geometric median and robust estimation in Banach spaces0.56711318%
6Wainwright (2019) High-dimensional Statistics: A Non-Asymptotic Viewpoint0.5113233%
7Hsu, Kakade, and Zhang (2012) A tail inequality for quadratic forms of subgaussian random vectors0.5112250%
8Manski (2007) Identification for Prediction and Decision0.5112250%
9Bühlmann and van de Geer (2011) Statistics for high-dimensional data: methods, theory and applications0.5112250%
10Angrist and Evans (1998) Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size0.51121100%

Showing the top 10 of 42 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Identification and Estimation of Dynamic Games with Unknown Information Structure0.73732
2Estimating Discrete Games of Complete Information: Bringing Logit Back in the Game0.73733
3Bounds for within-household encouragement designs with interference0.69351
42412.022510.40511
5Universal Inference for Incomplete Discrete Choice Models0.40511
6Binary Classification with the Maximum Score Model and Linear Programming0.40511
7Identifying the Effect of Persuasion0.00011