On strong deviation theorems concerning array of dependent random sequence

Ping Hu, Mengru Chen, Shu Chen and Zhong-zhi Wang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 9, 3098-3107

Abstract: Let ξ={ξni,1≤i≤n}n∈N be an array of random variables on the probability space (Ω,F,P). Let Q be another probability measure on F and, assume that under the law of Q, ξ is row-wise independent. Let h(P∥Q) be the sample-divergence rate of P with respect to Q related to ξ. A kind of strong deviation theorems, represented by h(P∥Q), of the arithmetic mean and the geometric mean of ξ are obtained. Moreover, no conditions are imposed on the joint distribution of ξ.

Date: 2023
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DOI: 10.1080/03610926.2021.1967396

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