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

Babii, Andrii (2017) Honest confidence sets in nonparametric IV regression and other ill-posed models. TSE Working Paper, n. 17-803, Toulouse

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Official URL: http://tse-fr.eu/pub/31687

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.

Item Type: Monograph (Working Paper)
Language: English
Date: May 2017
Place of Publication: Toulouse
Uncontrolled Keywords: nonparametric instrumental regression, functional linear regression, density deconvolution, honest uniform confidence sets, non-asymptotic inference, ill-posed models, Tikhonov regularization
JEL codes: C14 - Semiparametric and Nonparametric Methods
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 15 May 2017 13:17
Last Modified: 07 Mar 2018 13:24
OAI ID: oai:tse-fr.eu:31687
URI: http://publications.ut-capitole.fr/id/eprint/24049

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