On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. For local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentized is used. In addition, we derive coverage error optimal bandwidths for both conventional and robust bias-corrected confidence intervals, and discuss easy-to-implement bandwidth selectors. We also show that the MSE-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction only at interior points when second-order (equivalent) kernels are employed, but is otherwise suboptimal both at interior and boundary points because it is too "large". All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices.