  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.
