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Asymptotic Distributions of Weighted U-Statistics of Degree 2

Kevin A. O'Neil and Richard A. Redner
The Annals of Probability
Vol. 21, No. 2 (Apr., 1993), pp. 1159-1169
Stable URL: http://www.jstor.org/stable/2244694
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Distributions of Weighted U-Statistics of Degree 2
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Abstract

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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