Before revision:  First, we establish noveluniformly valid Edgeworth expansions for nonparametric local polynomial regression, offering some technical results that may be of independent interest, and use them to characterize the coverage error of and rank confidence interval estimatorsfor the regression function and its derivatives. As a second application we consider inference in least squares linear regression under potential misspecification, ranking interval estimators utilizing uniformly valid expansions already established in the literature.
After revision:  First, we establish noveluniformly 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.