Convergence Rates for $U$-Statistics and Related Statistics
Grams, William F. ; Serfling, R. J.
Ann. Statist., Tome 1 (1973) no. 2, p. 153-160 / Harvested from Project Euclid
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Bounds are provided for the rates of convergence in the central limit theorem and the strong law of large numbers for $U$-statistics. The results are obtained by establishing suitable bounds upon the moments of the difference between a $U$-statistic and its projection. Analogous conclusions for the associated von Mises statistical functions are indicated. Statistics considered for exemplification are the sample variance and the Wilcoxon two-sample statistic.
Publié le : 1973-01-14
Classification:  
@article{1193342392,
     author = {Grams, William F. and Serfling, R. J.},
     title = {Convergence Rates for $U$-Statistics and Related Statistics},
     journal = {Ann. Statist.},
     volume = {1},
     number = {2},
     year = {1973},
     pages = { 153-160},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1193342392}
}

Grams, William F.; Serfling, R. J. Convergence Rates for $U$-Statistics and Related Statistics. Ann. Statist., Tome 1 (1973) no. 2, pp.  153-160. http://gdmltest.u-ga.fr/item/1193342392/