Before revision:  The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals , uniformly over some empirically-relevant class of data generating processes. The framework employs the "check" function to quantify coverage error loss, which allows researchers to incorporate their preference in terms of over- and under-coverage, where confidence intervals attaining the best-possible uniform coverage error are minimax optimal. We demonstrate the usefulness of our framework with three distinct applications. 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.
After revision:  The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals , 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.