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

TL;DR

This paper develops uniform inference methods for nonparametric series regression that remain valid despite the common practice of searching over the number of series terms, ensuring reliable confidence intervals and bands.

Contribution

It introduces inference procedures that are uniform in the number of series terms, accommodating data-dependent model selection in nonparametric series estimation.

Findings

Methods achieve valid asymptotic coverage probabilities.

Finite sample performance is demonstrated through simulations.

Application to wage elasticity estimation illustrates practical utility.

Abstract

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).