RT Monograph
SR 00
A1 Babii, Andrii
T1 Honest confidence sets in nonparametric IV regression and other ill-posed models
YR 2017
FD 2017-05
VO 17-803
SP 56
K1 nonparametric instrumental regression
K1 functional linear regression
K1 density deconvolution
K1 honest uniform confidence sets
K1 non-asymptotic inference
K1 ill-posed models
K1 Tikhonov regularization
AB 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.
T2 TSE Working Paper
PB TSE Working Paper
PP Toulouse
AV Published
LK https://publications.ut-capitole.fr/id/eprint/24049/
UL http://tse-fr.eu/pub/31687