Before revision: We characterize the minimax bound on coverage error of Wald-type confidence intervals for nonparametric local polynomial regression . This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function.
After revision: We characterize the minimax bound on coverage error of Wald-type confidence intervals for nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for t statistics and coverage error expansions for interval estimators that (i) hold uniformly in the data generating process, (ii) allow for the uniform kernel, and (iii) cover estimation of derivatives of the regression function. The terms of the higher-order expansions, and their associated rates as a function of the sample size and bandwidth sequence, depend on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function.