Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions

Miller, R. G.; Sen, Pranab Kumar

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 31-41 / Harvested from Project Euclid

Résumé

For partial cumulative sums of independent and identically distributed random variables (i.i.d.r.v.) with a finite (positive) variance, weak convergence to Brownian motion processes has been established by Donsker (1951, 1952). The result is extended here to differentiable statistical functions of von Mises (1947) and $U$-statistics of Hoeffding (1948). Along with the extension to generalized $U$-statistics, a few applications are briefly sketched.

Publié le : 1972-02-14
Classification:

@article{1177692698,
     author = {Miller, R. G. and Sen, Pranab Kumar},
     title = {Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 31-41},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692698}
}

Miller, R. G.; Sen, Pranab Kumar. Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  31-41. http://gdmltest.u-ga.fr/item/1177692698/