Article ID Journal Published Year Pages File Type
1148234 Journal of Statistical Planning and Inference 2008 9 Pages PDF
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/ψ(logn)2 with any ψ>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
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