Marcinkiewicz–Zygmund strong laws for -statistics of weakly dependent observations |
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| Authors: | Herold G Dehling Olimjon Sh Sharipov |
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| Institution: | aFakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany;bDepartment of Probability Theory and Mathematical Statistics, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, 29 Dormon Yoli Street, Tashkent 100125, Uzbekistan |
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| Abstract: | We prove the Marcinkiewicz–Zygmund Strong Law of Large Numbers for U-statistics of strictly stationary, absolutely regular observations (ξi)i≥1. Under suitable moment conditions and conditions on the mixing rate, we show that for some γ≥0, in the non-degenerate case, and in the degenerate case. |
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