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Parameter estimated standardized \(U\)-statistics. (English) Zbl 1342.60047

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

Citations:

Zbl 0956.62042
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