Asymptotic Distribution of Symmetric Statistics
Rubin, H. ; Vitale, R. A.
Ann. Statist., Tome 8 (1980) no. 1, p. 165-170 / Harvested from Project Euclid
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Sequences of $m$th order symmetric statistics are examined for convergence in law. Under appropriate conditions, a limiting distribution exists and is equivalent to that of a linear combination of products of Hermite polynomials of independent $N(0, 1)$ random variables. Connections with the work of von Mises, Hoeffding, and Filippova are noted.
Publié le : 1980-01-14
Classification:  Symmetric statistics,  Hermite polynomials,  von Mises statistics,  $U$-statistics,  60F05,  62E20 
@article{1176344898,
     author = {Rubin, H. and Vitale, R. A.},
     title = {Asymptotic Distribution of Symmetric Statistics},
     journal = {Ann. Statist.},
     volume = {8},
     number = {1},
     year = {1980},
     pages = { 165-170},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176344898}
}

Rubin, H.; Vitale, R. A. Asymptotic Distribution of Symmetric Statistics. Ann. Statist., Tome 8 (1980) no. 1, pp.  165-170. http://gdmltest.u-ga.fr/item/1176344898/