Improved Inference for Nonparametric Regression

Abstract

Nonparametric regression and regression-discontinuity designs suffer from smoothing bias that distorts conventional confidence intervals. Solutions based on robust bias correction (RBC) are now central to the economist's toolbox. In this paper, we establish a novel connection between RBC methods and bootstrap prepivoting. Revisiting RBC through the lens of bootstrapping allows us to develop a novel bias correction procedure which delivers improved nonparametric inference. The resulting confidence intervals are 17% shorter than the usual intervals employed in curve estimation and regression discontinuity designs, without compromising asymptotic coverage. This holds regardless of evaluation point location, bandwidth choice, or regressor and error distribution.

Figures (3)

• Figure 1: Nonparametric curves: original (), LP bootstrap ( ), and GP bootstrap ( )
• Figure 2: The functions $\mathsf{w}_{\mathsf{PLP}}$ () and $\mathsf{w}_{\mathsf{RBC}}$ ( ) for five kernels
• Figure 3: The functions $\mathsf{w}_{\mathsf{mPLP}}$ () and $\mathsf{w}_{\mathsf{RBC}}$ ( ) for five kernels -- boundary case