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On tail probabilities of Kolmogorov-Smirnov statistic based on strong mixing processes

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  • Krishnaiah, Y. S. Rama

Abstract

For a strictly stationary sequence {Xi} define , where Fn and F are the empirical distribution function (d.f.) and common d.f. pertaining to {Xi}. Sen (1974, Theorem 3.2) established the tail probability inequalities for Dn when {Xn} is [phi]-mixing process. In the present paper, it is proved that Sen's result remains to be true for a class of stro mixing processs also which include [phi]-mixing and the asymptotically uncorrelated processes as special cases. Some applications are given.

Suggested Citation

  • Krishnaiah, Y. S. Rama, 1993. "On tail probabilities of Kolmogorov-Smirnov statistic based on strong mixing processes," Statistics & Probability Letters, Elsevier, vol. 16(5), pages 369-377, April.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:5:p:369-377
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    Cited by:

    1. Kim, Tae Yoon, 1999. "On tail probabilities of Kolmogorov-Smirnov statistics based on uniform mixing processes," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 217-223, July.
    2. Jin Zhang & Yuehua Wu, 2002. "Beta Approximation to the Distribution of Kolmogorov-Smirnov Statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 577-584, September.

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