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Nonparametric series regression often involves specification search over thetuning parameter, i.e., evaluating estimates and confidence intervals with adifferent number of series terms. This paper develops pointwise and uniforminferences for conditional mean functions in nonparametric series estimationsthat are uniform in the number of series terms. As a result, this paperconstructs confidence intervals and confidence bands with possiblydata-dependent series terms that have valid asymptotic coverage probabilities.This paper also considers a partially linear model setup and develops inferencemethods for the parametric part uniform in the number of series terms. Thefinite sample performance of the proposed methods is investigated in varioussimulation setups as well as in an illustrative example, i.e., thenonparametric estimation of the wage elasticity of the expected labor supplyfrom Blomquist and Newey (2002).

Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms