An Exponential Inequality for Strictly Stationary and Negatively Associated Random Variables

作者：Xing, Guodong^*; Yang, Shanchao

来源：Communications in Statistics - Theory and Methods, 2010, 39(2): 340-349.

DOI：10.1080/03610920902750053

• Exponential inequality
• Convergence rate
• Negatively associated

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)(log n)(1/2) for the strong law of large numbers that Sigma(n)(i=1) (X-i - EXi)/n -> 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)p(n)(1/2)(log n)(3/2), and n(-1/2)(log n)(1/2)(log log n)(xi/2) for any xi > 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.

• 出版日期2010
• 单位湖南科技学院; 广西师范大学