Extrapolation techniques in U-statistic variance estimation

ABSTRACT

This article considers the problem of variance estimation of a U-statistic. Following the proposal of a linearly extrapolated variance estimator in Wang and Chen (2015), we consider a second-order extrapolation technique and devise a variance estimator that is nearly second-order unbiased. Simulation studies confirm that the second-order extrapolated variance estimator has smaller bias than the linearly extrapolated variance estimator and the jackknife variance estimator across a wide selection of distributions. In addition, the proposal also yields a smaller mean squared error than its counterparts. In the end, we discuss the advantages of the proposed variance estimator in regression analysis and model selection.

KEYWORDS:

• Hoeffding-decomposition
• Linear extrapolation
• Non linear extrapolation
• Unbiased
• U-statistic
• Variance estimation.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G