Coverage Error Optimal Confidence Intervals for Local Polynomial Regression

In this paper we develop new confidence intervals for local polynomial regression, which minimize their worse-case coverage error and length in large samples. Our results rely on novel, valid Edgeworth expansions for $t$-statistics based on local polynomial methods, which are established uniformly over relevant classes of data generating processes and interval estimators. These higher-order expansions also allow for the uniform kernel and any derivative order, significantly improving on previous technical results available in the literature. In addition, we discuss principled, inference-optimal tuning parameter (bandwidth) selection and kernel functions. The main methodological results obtained in this paper are implemented in companion {\sf R} and \texttt{Stata} software packages.