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Honest Confidence Sets in Nonparametric IV Regression and Other Ill-Posed Models

Andrii Babii

arXiv 9 Nov 2016 · Mathematics — Statistics Theory · 4 citations (OpenAlex)

arXiv:1611.03015 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, i.e., constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. Using U.S. data, we provide uniform confidence sets for Engel curves for various commodities.

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54
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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
1V. Chernozhukov, D. Chetverikov, and K. Kato (2016) Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related gaussian couplings1.00064100%
2A. Babii and J.-P. Florens (2020) Is completeness necessary? estimation in nonidentified linear models1.00063100%
3S. Darolles, Y. Fan, J. Florens, and E. Renault Nonparametric instrumental regression1.00063100%
4V. Chernozhukov, D. Chetverikov, and K. Kato Gaussian approximation of suprema of empirical processes1.00053100%
5S. Boucheron, G. Lugosi, and P. Massart (2013) Concentration Inequalities0.84333100%
6R. Blundell, X. Chen, and D. Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves0.81142100%
7M. Carrasco, J.-P. Florens, and E. Renault (2007) Chapter 77: Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization0.81142100%
8A. B. Tsybakov (2009) Introduction to nonparametric estimation0.81142100%
9A. Babii (2020) High-dimensional mixed-frequency iv regression0.73732100%
10R. M. Dudley (2016) V.n. sudakov's work on expected suprema of gaussian processes0.73732100%

Showing the top 10 of 54 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
1High-dimensional mixed-frequency IV regression0.64422
2Are Unobservables Separable?0.51121
3One-step smoothing splines instrumental regression0.51121
42503.126110.51121
5Adaptive estimation for some nonparametric instrumental variable models0.40511
6Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities0.40511
7Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity0.40511