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

Gutti Jogesh Babu; Kesar Singh

doi:10.1016/0047-259X(82)90060-4

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

Gutti Jogesh Babu
, Kesar Singh

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	508-525
Number of pages	18
Journal	Journal of Multivariate Analysis
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/0047-259X(82)90060-4
State	Published - Dec 1982

All Science Journal Classification (ASJC) codes

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/0047-259X(82)90060-4

Cite this

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

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.",

author = "Babu, \{Gutti Jogesh\} and Kesar Singh",

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AU - Singh, Kesar

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AB - 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.

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UR - https://www.scopus.com/pages/publications/49049141940#tab=citedBy

U2 - 10.1016/0047-259X(82)90060-4

DO - 10.1016/0047-259X(82)90060-4

M3 - Article

AN - SCOPUS:49049141940

SN - 0047-259X

VL - 12

SP - 508

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JO - Journal of Multivariate Analysis

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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