Extrapolation techniques in U-statistic variance estimation |
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Authors: | Qing Wang |
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Institution: | Department of Mathematics, Wellesley College, Wellesley, MA, USA |
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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 Wang, Q., Chen, S. (2015). A general class of linearly extrapolated variance estimators. Stat. Probab. Lett. 98:29–38.Crossref], Web of Science ®] , Google Scholar]), 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. |
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Keywords: | Hoeffding-decomposition Linear extrapolation Non linear extrapolation Unbiased U-statistic Variance estimation |
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