Empirical distribution functions and functions of order statistics for mixing random variables

DOI10.1016/0047-259X(80)90061-5zbMath0466.62043OpenAlexW2061172442MaRDI QIDQ1155315

Madan Lal Puri, Lanh Tat Tran

Publication date: 1980

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(80)90061-5

zbMATH Keywords

order statisticsasymptotic normalitystrong mixingstrong laws of large numbersempirical distribution functionsphi-mixingfunctions of order statistics

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (6)

Weighted approximations of tail processes for \(\beta\)-mixing random variables. ⋮ Order statistics for nonstationary time series ⋮ Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours ⋮ Rank order statistics for time series models ⋮ Some characterizations of almost sure bounds for weighted multidimensional empirical distributions and a Glivenko-Cantelli theorem for sample quantiles ⋮ The empirical distribution function and strong laws for functions of order statistics of uniform spacings

Cites Work

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• On functions of order statistics for mixing processes
• Weak convergence of generalized empirical processes relative to \(d_q\) under strong mixing
• A functional law of the iterated logarithm for empirical distribution functions of weakly dependent random variables
• A Glivenko-Cantelli theorem and strong laws of large numbers for functions of order statistics
• A law of the iterated logarithm for functions of order statistics
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• A Generalization of the Glivenko-Cantelli Theorem
• Convergence of Distributions Generated by Stationary Stochastic Processes
• Functions of Order Statistics
• Some Limit Theorems for Stationary Processes

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