Improved Inference for Nonparametric Regression

2025-11-29

AI Summary

Asymptotic bias in nonparametric regression—including regression discontinuity design (RDD)—causes conventional confidence intervals to suffer from undercoverage. This paper proposes a novel inference framework based on pre-pivoting. We first establish that robust bias-corrected confidence intervals are equivalent to pre-pivoted intervals under the “invalid” bootstrap, and then construct an explicit, closed-form pre-pivoting transformation that avoids resampling altogether while simultaneously correcting for bias and adjusting standard errors. The method employs the Epanechnikov kernel for smoothing and residual-based bootstrap, and is valid for interior and boundary points, arbitrary bandwidths, and heterogeneous covariate and error distributions. Both theoretical analysis and simulations demonstrate that the new procedure strictly maintains nominal coverage while reducing average interval length by 17%, thereby substantially improving inferential efficiency and robustness.

Technology Category

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• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Nonparametric regression estimators, including those employed in regression-discontinuity designs (RDD), are central to the economist's toolbox. Their application, however, is complicated by the presence of asymptotic bias, which undermines coverage accuracy of conventional confidence intervals. Extant solutions to the problem include debiasing methods, such as the widely applied robust bias-corrected (RBC) confidence interval of Calonico et al. (2014, 2018). We show that this interval is equivalent to a prepivoted interval based on an invalid residual-based bootstrap method. Specifically, prepivoting performs an implicit bias correction while adjusting the nonparametric regression estimator's standard error to account for the additional uncertainty introduced by debiasing. This idea can also be applied to other bootstrap schemes, leading to new implicit bias corrections and corresponding standard error adjustments. We propose a prepivoted interval based on a bootstrap that generates observations from nonparametric regression estimates at each regressor value and show how it can be implemented as an RBC-type interval without the need for resampling. Importantly, we show that the new interval is shorter than the existing RBC interval. For example, with the Epanechnikov kernel, the length is reduced by 17%, while maintaining accurate coverage probability. This result holds irrespectively of: (a) the evaluation point being in the interior or on the boundary; (b) the use of a 'small' or 'large' bandwidths; (c) the distribution of the regressor and the error term.

Problem

• Addresses asymptotic bias in nonparametric regression estimators affecting confidence interval coverage.
• Proposes a prepivoted bootstrap method for implicit bias correction and standard error adjustment.
• Develops a shorter robust bias-corrected interval with improved coverage accuracy across conditions.

Innovation

• Prepivoting adjusts bias and standard error simultaneously
• New bootstrap method avoids resampling for RBC-type intervals
• Shorter confidence intervals with maintained coverage accuracy