Functional Limit Theorems for $U$-Processes
Nolan, Deborah ; Pollard, David
Ann. Probab., Tome 16 (1988) no. 4, p. 1291-1298 / Harvested from Project Euclid
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A $U$-process is a collection of $U$-statistics indexed by a family of symmetric kernels. In this paper, two functional limit theorems are obtained for sequences of standardized $U$-processes. In one case the limit process is Gaussian; in the other, the limit process has finite dimensional distributions of infinite weighted sums of $\chi^2$ random variables. Goodness-of-fit statistics provide examples.
Publié le : 1988-07-14
Classification:  $U$-statistics,  empirical processes,  functional limit theorems,  equicontinuity,  finite dimensional distributions,  goodness-of-fit statistics,  60F17,  62E20 
@article{1176991691,
     author = {Nolan, Deborah and Pollard, David},
     title = {Functional Limit Theorems for $U$-Processes},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 1291-1298},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991691}
}

Nolan, Deborah; Pollard, David. Functional Limit Theorems for $U$-Processes. Ann. Probab., Tome 16 (1988) no. 4, pp.  1291-1298. http://gdmltest.u-ga.fr/item/1176991691/