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April, 1993 Asymptotic Distributions of Weighted $U$-Statistics of Degree 2
Kevin A. O'Neil, Richard A. Redner
Ann. Probab. 21(2): 1159-1169 (April, 1993). DOI: 10.1214/aop/1176989286


The limiting distribution of weighted $U$-statistics of degree 2 is found for a wide class of weights, including uniform weights. Nonnormal limits can occur for both degenerate and nondegenerate kernels. A compact expression is given for the cumulants of the distribution. Incomplete and randomly weighted $U$-statistics are also analyzed.


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Kevin A. O'Neil. Richard A. Redner. "Asymptotic Distributions of Weighted $U$-Statistics of Degree 2." Ann. Probab. 21 (2) 1159 - 1169, April, 1993.


Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0774.62018
MathSciNet: MR1217584
Digital Object Identifier: 10.1214/aop/1176989286

Primary: 62E20
Secondary: 60F05

Keywords: $U$-statistics , Cumulants , incomplete $U$-statistics

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 2 • April, 1993
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