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Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications

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Abstract

In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on L p convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    DeMei Yuan & Jun An

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  1. DeMei Yuan
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  2. Jun An
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Correspondence to DeMei Yuan.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10871217) and the SCR of Chongqing Municipal Education Commission (Grant No. KJ090703)

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Yuan, D., An, J. Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications. Sci. China Ser. A-Math. 52, 1887–1904 (2009). https://doi.org/10.1007/s11425-009-0154-z

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  • DOI: https://doi.org/10.1007/s11425-009-0154-z

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