498 – Bayesian Nonparametrics, U-Statistics, Saddle Point, and Quantile Model
Extrapolation Techniques in U-Statistic Variance Estimation
Qing Wang
Williams College
This paper considers the problem of variance estimation of a U-statistic. Extrapolation techniques are proposed to overcome the drawback of having negative values when using the unbiased U-statistic variance estimator (Wang and Lindsay, 2014). Following the proposal of the linearly extrapolated variance estimator in Wang and Chen (2015), we consider nonlinear extrapolation method and devise a variance estimator that is nearly second-order unbiased. Simulation studies indicate that the second-order extrapolated variance estimator has smaller mean squared error compared to the unbiased variance estimator and the jackknife variance estimator across a wide selection of distributions. We also discuss the advantage of the proposal compared to its jackknife counterpart in regression analysis and model selection.