We propose a framework for ranking confidence interval estimators in terms of their uniform coverage accuracy. 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. 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. Third, we study heteroskedasticity-autocorrelation robust inference to showcase how our framework can unify existing conclusions. Several other potential applications are mentioned{\sf    .
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 andStata software packages .
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We propose a framework for ranking confidence interval estimators in terms of their uniform coverage accuracy. The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals
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
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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
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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
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
R
Third, we study heteroskedasticity-autocorrelation robust inference to showcase how our framework can unify existing conclusions. Several other potential applications are mentioned
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
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R
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Stata
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software packages