Honest confidence sets in nonparametric IV regression and other ill-posed models

Andrii Babii

No 17-803, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: This paper provides novel methods for inference in a very general class of ill-posed models in econometrics, encompassing the nonparametric instrumental regression, different functional regressions, and the deconvolution. I focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). I first show that it is not possible to develop inferential methods directly based on the uniform central limit theorem. To circumvent this difficulty I develop two approaches that lead to valid confidence sets. I characterize expected diameters and coverage properties uniformly over a large class of models (i.e. constructed confidence sets are honest). Finally, I illustrate that introduced confidence sets have reasonable width and coverage properties in samples commonly used in applications with Monte Carlo simulations and considering application to Engel curves.

Keywords: nonparametric instrumental regression; functional linear regression; density deconvolution; honest uniform confidence sets; non-asymptotic inference; ill-posed models; Tikhonov regularization (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Date: 2017-05
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS (2020)
Working Paper: Honest Confidence Sets in Nonparametric IV Regression and Other Ill-Posed Models (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:31687

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