  Nonparametric series regression often involves specification search over the
tuning parameter, i.e., evaluating estimates and confidence intervals with a
different number of series terms. This paper develops pointwise and uniform
inferences for conditional mean functions in nonparametric series estimations
that are uniform in the number of series terms. As a result, this paper
constructs confidence intervals and confidence bands with possibly
data-dependent series terms that have valid asymptotic coverage probabilities.
This paper also considers a partially linear model setup and develops inference
methods for the parametric part uniform in the number of series terms. The
finite sample performance of the proposed methods is investigated in various
simulation setups as well as in an illustrative example, i.e., the
nonparametric estimation of the wage elasticity of the expected labor supply
from Blomquist and Newey (2002).
