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This paper develops inferential methods for a very general class of ill-posedmodels in econometrics encompassing the nonparametric instrumental variableregression, various functional regressions, and the density deconvolution. Wefocus on uniform confidence sets for the parameter of interest estimated withTikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011).Since it is impossible to have inferential methods based on the central limittheorem, we develop two alternative approaches relying on the concentrationinequality and bootstrap approximations. We show that expected diameters andcoverage properties of resulting sets have uniform validity over a large classof models, i.e., constructed confidence sets are honest. Monte Carloexperiments illustrate that introduced confidence sets have reasonable widthand coverage properties. Using U.S. data, we provide uniform confidence setsfor Engel curves for various commodities.

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