TY - UNPB

T1 - Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing

AU - Kang, Byunghoon

PY - 2017/5

Y1 - 2017/5

N2 - Existing asymptotic theory for inference in nonparametric series estimation typically imposes an undersmoothing condition that the number of series terms is sufficiently large to make bias asymptotically negligible. However, there is no formally justified data-dependent method for this in practice. This paper constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide an empirical process theory for the t-statistics indexed by the number of series terms. Using this result, I show that test based on the infimum of the t-statistics and its asymptotic critical value controls asymptotic size with undersmoothing condition. Using this test, we can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Allowing asymptotic bias without the undersmoothing condition, I show that CI based on the infimum of the t-statistics bounds coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on the standard CI with the possible ad hoc choice of series terms.

AB - Existing asymptotic theory for inference in nonparametric series estimation typically imposes an undersmoothing condition that the number of series terms is sufficiently large to make bias asymptotically negligible. However, there is no formally justified data-dependent method for this in practice. This paper constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide an empirical process theory for the t-statistics indexed by the number of series terms. Using this result, I show that test based on the infimum of the t-statistics and its asymptotic critical value controls asymptotic size with undersmoothing condition. Using this test, we can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Allowing asymptotic bias without the undersmoothing condition, I show that CI based on the infimum of the t-statistics bounds coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on the standard CI with the possible ad hoc choice of series terms.

KW - Nonparametric series regression

KW - Pointwise confidence interval

KW - Smoothing parameter choice

KW - Specification search

KW - Undersmoothing

M3 - Working paper

T3 - Economics Working Paper Series

BT - Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing

PB - Lancaster University, Department of Economics

CY - Lancaster

ER -