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On the asymptotic independence of the sum and rare values of weakly dependent stationary random variables

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  • Hsing, Tailen

Abstract

It is shown that if the stationary sequence {Xi} has finite variance and satisfies a certain mixing condition, then the asymptotic distribution of [summation operator]ni=1 Xn is unaffected by the information of whether the summands are in certain "rare" sets. An application of the result shows that [summation operator]ni=1 Xi and the extremes of X1,...,Xn are asymptotically independent. This is in sharp contrast to the infinite variance case.

Suggested Citation

  • Hsing, Tailen, 1995. "On the asymptotic independence of the sum and rare values of weakly dependent stationary random variables," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 49-63, November.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:49-63
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    Cited by:

    1. Saralees Nadarajah & Emmanuel Afuecheta & Stephen Chan, 2019. "Ordered random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 344-366, March.
    2. Arendarczyk, Marek & Kozubowski, Tomasz. J. & Panorska, Anna K., 2018. "The joint distribution of the sum and maximum of dependent Pareto risks," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 136-156.

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