The Role of Jackknife Estimation in Reducing Bias and Improving Variance Estimates in Resampled Datasets

Posted: Jul 09, 2014

• James Gonzalez
• James Young
• Zoey Baker

Abstract

Resampling methods have revolutionized statistical inference and machine learning by providing powerful tools for estimating sampling distributions, assessing model performance, and quantifying uncertainty. Among these methods, bootstrap techniques and cross-validation procedures have gained widespread adoption across numerous disciplines. However, despite their utility, these approaches are not without limitations. Bootstrap methods, while asymptotically consistent, can exhibit significant finite-sample biases, particularly in complex estimation scenarios. Similarly, cross-validation procedures often suffer from variance issues that can lead to unstable performance estimates. The jackknife method, originally introduced by Quenouille for bias reduction and later extended by Tukey for variance estimation, represents an alternative resampling approach that has received comparatively less attention in contemporary statistical practice. The fundamental principle underlying jackknife estimation involves systematically leaving out one observation at a time from the dataset and recalculating the statistic of interest, thereby generating a distribution of estimates that can be used to assess bias and variance. This research addresses a critical gap in the literature by developing a comprehensive framework that integrates jackknife estimation with traditional resampling methods. Our approach leverages the unique properties of jackknife estimators to mitigate biases inherent in bootstrap procedures while simultaneously improving variance estimates in cross-validation settings. The novelty of our work lies in the systematic derivation of jackknife-enhanced resampling algorithms that adapt to various data structures and estimation problems.