Article

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

Statistics & Probability Lettersjournal2009en

ABI

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 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.

Topics

Probability and Risk Models Financial Risk and Volatility Modeling Stochastic processes and financial applications

Identifiers

DOI: 10.1016/j.spl.2009.06.012

Citations and references

Cited by 1 14 references

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