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

Andrii Babii

Papers from arXiv.org

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.

Date: 2016-11, Revised 2020-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published in Econometric Theory , 36(4), 2020, pp. 658-706

Downloads: (external link)
http://arxiv.org/pdf/1611.03015 Latest version (application/pdf)

Related works:
Journal Article: HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS (2020)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1611.03015

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().