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We consider the problem of constructing honest conﬁdence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp eﬀiciency bounds of using diﬀerent kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum meansquared error results in CIs that are nearly eﬀicient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n -4/5 , the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in an empirical application.
Armstrong, Timothy B. and Kolesár, Michal, "Simple and Honest Confidence Intervals in Nonparametric Regression" (2016). Cowles Foundation Discussion Papers. 2498.