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On r-quick limit sets for empirical and related processes based on mixing random variables

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  • Babu, Gutti Jogesh
  • Singh, Kesar

Abstract

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results are applied to linear functions of order statistics. Some results on r-quick convergence of certain Gaussian processes are also established.

Suggested Citation

  • Babu, Gutti Jogesh & Singh, Kesar, 1982. "On r-quick limit sets for empirical and related processes based on mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 508-525, December.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:4:p:508-525
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