Extrapolation Techniques in U-Statistic Variance Estimation

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Qing Wang*
• Companies: Williams College
• Keywords: Hoeffding-decomposition ; linear extrapolation ; nonlinear extrapolation ; variance estimation ; unbiased ; U-statistic

Abstract

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.