Nikitin, Ya. Yu.; Ponikarov, E. V. 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)]. Reviewer: Neville Weber (Sydney) Cited in 5 Documents MSC: 60F10 Large deviations Keywords:U-statistics; V-statistics; Chernoff large deviations Citations:Zbl 0565.60023 PDFBibTeX XMLCite \textit{Ya. Yu. Nikitin} and \textit{E. V. Ponikarov}, Dokl. Math. 60, No. 3, 10--12 (1999; Zbl 1041.60027); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 369, No. 1, 10--12 (1999)