Empirical Edgeworth expansions for symmetric statistics
Putter, Hein ; van Zwet, Willem R.
Ann. Statist., Tome 26 (1998) no. 3, p. 1540-1569 / Harvested from Project Euclid
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In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including $U$-statistics, $L$-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap in the case of a $U$-statistic of degree two.
Publié le : 1998-08-14
Classification:  Edgeworth expansion,  Hoeffding’s decomposition,  jackknife,  boot-strap,  62E20,  62G09 
@article{1024691253,
     author = {Putter, Hein and van Zwet, Willem R.},
     title = {Empirical Edgeworth expansions for symmetric statistics},
     journal = {Ann. Statist.},
     volume = {26},
     number = {3},
     year = {1998},
     pages = { 1540-1569},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1024691253}
}

Putter, Hein; van Zwet, Willem R. Empirical Edgeworth expansions for symmetric statistics. Ann. Statist., Tome 26 (1998) no. 3, pp.  1540-1569. http://gdmltest.u-ga.fr/item/1024691253/