A general class of linearly extrapolated variance estimators

A general class of linearly extrapolated variance estimators was developed as an extension of the conventional leave-one-out jackknife variance estimator. In the context of U-statistic variance estimation, the proposed variance estimator is first-order unbiased. After showing the equivalence between the Hoeffding decomposition (Hoeffding, 1948) and the ANOVA decomposition (Efron and Stein, 1981), we study the bias property of the proposed variance estimator in comparison to the conventional jackknife method. Simulation studies indicate that the proposal has comparable performance to the jackknife method when assessing the variance of the sample variance in various distributions. An application to half-sampling cross-validation indicates that the proposal is more computationally efficient and shows better performance than its jackknife counterpart in the context of regression analysis.