Weak convergence of serial rank statistics under dependence with applications in time series and Markov processes

DOI10.1214/aop/1176990749zbMath0705.62083OpenAlexW2078615375MaRDI QIDQ918102

Michel Harel, Madan Lal Puri

Publication date: 1990

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176990749

zbMATH Keywords

weak convergenceasymptotic normalitytime seriesSkorokhod topologystrong mixingcontiguityARMA processesgeometrically ergodicphi-mixingDoeblin recurrentgraduate empirical processgraduate rank processlinear serial rank statisticstesting white noise against alternatives of ARMA serial dependence

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) Discrete-time Markov processes on general state spaces (60J05)

Related Items (4)

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes ⋮ The space \(\tilde D_ k\) land weak convergence for the rectangle-indexed processes under mixing ⋮ Some asymptotic results for a broad class of nonparametric statistics ⋮ Limiting behavior of one sample rank order statistics with unbounded scores for nonstationary absolutely regular processes

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