On the exponential inequalities for strictly stationary and negatively associated random variables

Some exponential inequalities for strictly stationary and negatively associated random variables are established. These inequalities improve the corresponding results which Jabbari Nooghabi and Azarnoosh [2009. Exponential inequality for negatively associated random variables. Statist. Papers 50, 419–428] and Oliveira [2005. An exponential inequality for associated variables. Statist. Probab. Lett. 73, 189–197] got. As application, we obtain the rate of convergence n - 1 / 2 ( log log n ) 1 / 2 ( log n ) 3 / 2 for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Jabbari Nooghabi and Azarnoosh [2009. Exponential inequality for negatively associated random variables. Statist. Papers 50, 419–428] only got n - 1 / 3 ( log n ) 5 / 3 for the case mentioned above.