Korolyuk, V. S.; Borovskikh, Yu. V. 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. Reviewer: R.Helmers (Amsterdam) MSC: 62E20 Asymptotic distribution theory in statistics 60F05 Central limit and other weak theorems 60F15 Strong limit theorems Keywords:central limit theorem; Berry-Esseen bound; limit theorems for UH- statistics; U-statistics; kernel; separable, real Hilbert space PDF BibTeX XML Cite \textit{V. S. Korolyuk} and \textit{Yu. V. Borovskikh}, Sov. Math., Dokl. 40, No. 2, 432--435 (1990; Zbl 0719.62030); translation from Dokl. Akad. Nauk SSSR 308, No. 6, 1301--1304 (1989)