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Large deviations of Chernoff type for \(U\)- and \(V\)-statistics. (English. Russian original) Zbl 1041.60027

Dokl. Math. 60, No. 3, 316-318 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 369, No. 1, 10-12 (1999).
This paper provides the first general results on Chernoff type large deviations for \(U\)-statistics and \(V\)-statistics for both the non-degenerate and weakly degenerate cases. The non-degenerate result for \(U\)-statistics corrects a related result by R. Dasgupta [Sankhyā, Ser. A 46, 110-116 (1984; Zbl 0565.60023)].

MSC:

60F10 Large deviations

Citations:

Zbl 0565.60023
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