Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

DOI10.1016/0047-259X(89)90066-3zbMath0693.62023MaRDI QIDQ908623

Michel Harel, Madan Lal Puri

Publication date: 1989

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

zbMATH Keywords

asymptotic normalityBrownian motionARMA processU-statisticaperiodicgeometrically ergodicrank order statisticdependent, nonidentically distributed continuous random variablesDoeblin recurrent Markov chainHarris recurrent

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Convergence of probability measures (60B10)

Related Items (7)

Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables ⋮ Weak convergence of weighted multivariate empirical U-statistics processes under mixing condition ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ Weak invariance of generalized U-statistics for nonstationary absolutely regular processes ⋮ Empirical U-statistics processes ⋮ Weak convergence for rectangle-indexed weighted multivariate empirical \(U\)-statistic processes under mixing conditions ⋮ Limiting behavior of one sample rank order statistics with unbounded scores for nonstationary absolutely regular processes

Cites Work

• Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory
• Limiting behavior of U-statistics, V-statistics, and one sample rank order statistics for nonstationary absolutely regular processes
• SUR UN MODÉLE AUTORÉGRESSIF NON LINÉAIRE, ERGODICITÉ ET ERGODICITÉ GÉOMÉTRIQUE
• Mixing Conditions for Markov Chains
• Unnamed Item

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