Abstract
We consider inference for (possibly) non-linear conditional expectations in the setup of nonparametric regression and regression-discontinuity designs. In this context, inference is challenging due to asymptotic bias of local polynomial estimators. We propose a novel approach to restore valid inference by means of proper implementations of the bootstrap. Specifically, we show conditions under which, even if the bootstrap test statistic is not able to mimic the behavior of the asymptotic bias -- making the bootstrap fail using standard arguments -- the large sample distribution of the bootstrap p-value only depends on some nuisance parameters which are easily estimable. We introduce two bootstrap algorithms, namely the local polynomial (LP) and fixed-local (FL) bootstrap, which deliver asymptotically valid confidence intervals (CIs) for both interior and boundary points without requiring undersmoothing or direct bias correction. We demonstrate the theoretical validity and analyze the efficiency properties of these methods, highlighting the asymptotic equivalence of the FL bootstrap-based CIs with robust bias correction (RBC) intervals, while showing that LP bootstrap-based CIs achieve greater efficiency. Monte Carlo simulations confirm the practical relevance of our methods.