An Exponential Inequality for Strictly Stationary and Negatively Associated Random Variables

摘要

We establish an exponential inequality for strictly stationary and negatively associated random variables which improves the corresponding results which Jabbari Nooghabi and Azarnoosh (2009) and Kim and Kim (2007) got, and get also the convergence rate n~(-1/2)2(log n)~(1/2) for the strong law of large numbers that Σ_(i=1)~n (X_i -EX_i)→ 0 a.s. without any extra condition on the covariance structure, which is faster than the relevant ones n~(-1/3)(log n)~(5/3), n~(1/2)2p_n~(1/2)(log n)~(3/2), and n~(-1/2)2(log n)~(1/2)2(log log n)~(ζ/2)2 for any ξ > 1 obtained by Jabbari Nooghabi and Azarnoosh (2009) for the case of geometrically decreasing covariance, Kim and Kim (2007) and Yang et al. (2008), respectively. In addition, an exponential inequality for the tail of a block decomposition of the sums is also presented, which improves the relevant one derived by Oliveira (2005) in the course of the proof.