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On the Glivenko-Cantelli theorem for generalized empirical processes based on strong mixing sequences

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  • Rama Krishnaiah, Y. S.

Abstract

Given \s{Xi, i [greater-or-equal, slanted] 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 [less-than-or-equals, slant] i [less-than-or-equals, slant] n and some [gamma] [epsilon] [0, 1], F1(x)=[gamma]P(Xi 0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing.

Suggested Citation

  • Rama Krishnaiah, Y. S., 1990. "On the Glivenko-Cantelli theorem for generalized empirical processes based on strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 10(5), pages 439-447, October.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:5:p:439-447
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    1. repec:hum:wpaper:sfb649dp2014-012 is not listed on IDEAS
    2. Jürgen Franke & Peter Mwita & Weining Wang, 2015. "Nonparametric estimates for conditional quantiles of time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 107-130, January.

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