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

摘要

Let {Y, Y_i, -∞ < i < ∞} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {a_i, -∞ < 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 {∑_(k = 1)~n ∑_(i = -∞)~∞ a_(i+k)Y_i~(1/t), n ≥ 1} 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 ρ~*-mixing sequences.