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Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions

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Let {Y, Yi, -¥ < i < ¥} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {ai, - ¥ < i < ¥} an absolutely summable sequence of real numbers. We are inspired by Wang et al. (Econometric Theory 18:119–139, 2002) and Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003). And Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003) have obtained Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions. In this paper, we prove the complete convergence of Pnk ¼1P1i ¼-1 - aiþkYi=n1=t; n - 1g under some suitable conditions. The results obtained improve and generalize the results of Li et al. (1992) and Zhang (1996). The results obtained extend those for negative associated sequences and q*-mixing sequences.

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