A Class of Linearly Extrapolated Variance Estimators

• Activity Number: 415
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shiwen Chen*+ and Qing Wang
• Companies: Williams College and Williams College
• Keywords: Jackknife ; Linear Extrapolation ; Resampling ; Variance Estimate

Abstract

In point estimation, the true parameter of interest theta of the population distribution F is usually estimated by a functional of the empirical distribution of n observations, denoted as hat{theta}_n = theta(hat{F}_n). In statistical practice, it is often important to learn about the sampling distribution or assess the precision of a point estimator by estimating its variance. The delete-one Jackknife variance estimator can be viewed as a linearly extrapolated variance estimator: one first constructs a variance estimator for subsamples of size n-1, and then extrapolates the estimation from sample size n-1 to n. In our study, we consider a general class of linearly extrapolated variance estimators, where the subsample size m can be less than or equal to n/2. We have verified the equivalence of ANOVA decomposition and Hoeffding decomposition, based on which we are able to compare the bias of various linearly extrapolated variance estimators for a general U-statistic. This class of estimators are first-order unbiased. In addition, the lowest bias is achieved by taking subsamples of size n/2.