An estimate of the closeness of the moments of \(UH\)-statistics under the conditions of the central limit theorem. (English. Russian original) Zbl 0748.60006

Korolyuk, V. S.; Borovskikh, Yu. V.

Theory Probab. Math. Stat. 42, 55-60 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 48-53 (1990).

The authors obtain an upper bound in the central limit theorem for the moments of non-degenerate \(U\)-statistics with Hilbert space valued kernels.

Reviewer: I.S.Borisov (Novosibirsk)

MSC:

60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
60F05	Central limit and other weak theorems
60F25	\(L^p\)-limit theorems

Keywords:

central limit theorem in Hilbert spaces; central limit theorem; non- degenerate \(U\)-statistics