Marcinkiewicz–Zygmund strong laws for -statistics of weakly dependent observations
Herold DehlingFakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, GermanyOlimjon Sh. SharipovDepartment of Probability Theory and Mathematical Statistics, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, 29 Dormon Yoli Street, Tashkent 100125, Uzbekistan
ABI
Аннотация
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 n−2+γ∑1≤i<j≤n(h(ξi,ξj)−Eh(ξ,η))→0 for some γ≥0, in the non-degenerate case, and n−1+γ∑1≤i<j≤n(h(ξi,ξj)−Eh(ξ,η))→0 in the degenerate case.
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