Asymptotic Distributions of Weighted $U$-Statistics of Degree 2
O'Neil, Kevin A. ; Redner, Richard A.
Ann. Probab., Tome 21 (1993) no. 4, p. 1159-1169 / Harvested from Project Euclid
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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.
Publié le : 1993-04-14
Classification:  Cumulants,  incomplete $U$-statistics,  $U$-statistics,  62E20,  60F05 
@article{1176989286,
     author = {O'Neil, Kevin A. and Redner, Richard A.},
     title = {Asymptotic Distributions of Weighted $U$-Statistics of Degree 2},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 1159-1169},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989286}
}

O'Neil, Kevin A.; Redner, Richard A. Asymptotic Distributions of Weighted $U$-Statistics of Degree 2. Ann. Probab., Tome 21 (1993) no. 4, pp.  1159-1169. http://gdmltest.u-ga.fr/item/1176989286/