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UH-statistics. (English. Russian original) Zbl 0719.62030
Sov. Math., Dokl. 40, No. 2, 432-435 (1990); translation from Dokl. Akad. Nauk SSSR 308, No. 6, 1301-1304 (1989).
Strong and weak limit theorems for UH-statistics are obtained. UH- statistics are defined in the same way as the familiar U-statistics, but now requiring only that the kernel function takes values in a separable, real Hilbert space, instead of being real-valued. Extending the theory of U-statistics the authors obtain strong laws, weak limit laws as well as a result of Berry-Esseen type for UH-statistics.
62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
60F15 Strong limit theorems