Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1148234 | Journal of Statistical Planning and Inference | 2008 | 9 Pages |
Abstract
We show some new exponential inequalities for strictly stationary and positively associated random variables being unbounded. These inequalities improve the corresponding results which Sung [2007. A note on the exponential inequality for associated random variables. Statist. Probab. Lett. 77, 1730-1736] got. As application, we obtain the rate of convergence n-1/2(loglogn)1/Ï(logn)2 with any Ï>2 for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm, while Sung [2007. A note on the exponential inequality for associated random variables. Statist. Probab. Lett. 77, 1730-1736] only got n-1/3logn for the case mentioned above.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Guodong Xing, Shanchao Yang,