Takahashi, Hiroshi; Yoshihara, Ken-ichi Parameter estimated standardized \(U\)-statistics. (English) Zbl 1342.60047 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 23, No. 3, 217-230 (2016). Summary: Extending the results of E. Gombay and L. Horváth [in: Asymptotic methods in probability and statistics. A volume in honour of Miklós Csörgő. ICAMPS ’97, an international conference at Carleton Univ., Ottawa, Ontario, Canada, July 1997. Amsterdam: North-Holland/ Elsevier. 563–576 (1998; Zbl 0956.62042)], we obtain a limit theorem for the maximum of standardized degenerate \(U\)-statistics defined by some absolutely regular sequences. MSC: 60F17 Functional limit theorems; invariance principles 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics 62G20 Asymptotic properties of nonparametric inference 62G05 Nonparametric estimation Keywords:standardized \(U\)-statistics; weak convergence; weakly dependent random variables; absolutely regular sequences Citations:Zbl 0956.62042 PDFBibTeX XMLCite \textit{H. Takahashi} and \textit{K.-i. Yoshihara}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 23, No. 3, 217--230 (2016; Zbl 1342.60047) Full Text: Link Link