On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables
AbstractThe object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur  holds for a stationary sequence of [phi]-mixing random variables. Two different orders of the remainder term, under different [phi]-mixing conditions, are obtained and used for proving two functional central limit theorems for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary [phi]-mixing processes.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 2 (1972)
Issue (Month): 1 (March)
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- Yves Dominicy & Siegfried Hörmann & Hiroaki Ogata & David Veredas, 2013.
"On sample marginal quantiles for stationary processes,"
ULB Institutional Repository
2013/136283, ULB -- Universite Libre de Bruxelles.
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