TY - UNPB

T1 - Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms

AU - Kang, Byunghoon

PY - 2018/3

Y1 - 2018/3

N2 - Nonparametric series estimation often involves specification search over the different number of series terms due to the unknown smoothness of underlying function. This paper considers pointwise inference in the nonparametric series regression for the conditional mean and introduces test based on the supremum of t-statistics over different series terms. I show that proposed test has correct asymptotic size and it can be used to construct confidence intervals that havecorrect asymptotic coverage probability uniform in the number of series terms. With possibly large bias in this setup, I also consider infimum of the t-statistics which is shown to reduce size distortions in such case. Asymptotic distribution of the test statistics, asymptotic size, and local power results are derived. I investigate the performance of the proposed tests and CIs in various simulation setups as well as an illustrative example, nonparametric estimation of wageelasticity of the expected labor supply from Blomquist and Newey (2002). I also extend our inference methods to the partially linear model setup.

AB - Nonparametric series estimation often involves specification search over the different number of series terms due to the unknown smoothness of underlying function. This paper considers pointwise inference in the nonparametric series regression for the conditional mean and introduces test based on the supremum of t-statistics over different series terms. I show that proposed test has correct asymptotic size and it can be used to construct confidence intervals that havecorrect asymptotic coverage probability uniform in the number of series terms. With possibly large bias in this setup, I also consider infimum of the t-statistics which is shown to reduce size distortions in such case. Asymptotic distribution of the test statistics, asymptotic size, and local power results are derived. I investigate the performance of the proposed tests and CIs in various simulation setups as well as an illustrative example, nonparametric estimation of wageelasticity of the expected labor supply from Blomquist and Newey (2002). I also extend our inference methods to the partially linear model setup.

KW - Nonparametric series regression

KW - Pointwise confidence interval

KW - Smoothing parameter choice

KW - Specification search

KW - Undersmoothing

M3 - Working paper

T3 - Economics Working Papers Series

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

PB - Lancaster University, Department of Economics

CY - Lancaster

ER -