Asymptotic equivalence of the jackknife and infinitesimal jackknife variance estimators for some smooth statistics

Bias, Consistency, and Alternative Perspectives of the Infinitesimal Jackknife

Though introduced nearly 50 years ago, the infinitesimal jackknife (IJ) remains a popular modern tool for quantifying predictive uncertainty in complex estimation settings. In particular, when supervised learning ensembles are constructed via bootstrap samples, recent work demonstrated that the IJ estimate of variance is particularly convenient and useful. However, despite the algebraic simplicity of its final form, its derivation is rather complex. As a result, studies clarifying the intuition behind the estimator or rigorously investigating its properties have been severely lacking. This wor…

Asymptotic accuracy of the jackknife variance estimator for certain smooth statistics

We show that that the jackknife variance estimator $v_{jack}$ and the the infinitesimal jackknife variance estimator are asymptotically equivalent if the functional of interest is a smooth function of the mean or a smooth trimmed L-statistic. We calculate the asymptotic variance of $v_{jack}$ for these functionals.

A Higher-Order Swiss Army Infinitesimal Jackknife

Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different weighted versions of the original dataset, which can be prohibitively time-consuming. For sufficiently regular optimization problems the optimum depends smoothly on the data weights, and so the process of repeatedly re-fitting can be approximated with a Taylor series that can be often evaluated relatively quickly. The first-order approximation is known as t…

用于方差的贝叶斯无穷小折刀法

The Bayesian Infinitesimal Jackknife for Variance

针对贝叶斯估计量频率学派协方差近似方法计算不便的问题，提出基于influence function的infinitesimal jackknife (IJ)方法，证明其可从单组后验样本高效计算且与经典方法渐近等价，并通过实验验证了其准确性与计算优势。