On the asymptotic distributions of partial sums of functionals of infinite-variance moving averages

DOI10.1214/aop/1022677460zbMath0961.60038OpenAlexW1519691648MaRDI QIDQ1568300

Tailen Hsing

Publication date: 28 May 2001

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

Full work available at URL: https://doi.org/10.1214/aop/1022677460

zbMATH Keywords

linear processstable processcentral and noncentral limit theorems

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (14)

Asymptotics of empirical processes of long memory moving averages with infinite variance. ⋮ Nonparametric regression under dependent errors with infinite variance ⋮ Localized level crossing random walk test robust to the presence of structural breaks ⋮ A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages ⋮ Nonparametric quantile regression with heavy-tailed and strongly dependent errors ⋮ Limit theorems for functionals of long memory linear processes with infinite variance ⋮ Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation ⋮ Memory properties of transformations of linear processes ⋮ Stable limits of empirical processes of moving averages with infinite variance. ⋮ \(M\)-estimation of linear models with dependent errors ⋮ Stable random fields, point processes and large deviations ⋮ Nonparametric density estimation for linear processes with infinite variance ⋮ On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation ⋮ On the effect of long-range dependence on extreme value copula estimation with fixed marginals

Cites Work

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• Central limit theorems for non-linear functionals of Gaussian fields
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• Convergence of empirical processes of mixing rv's on \([0,1\)]
• Parameter estimation for infinite variance fractional ARIMA
• Limit theorems for functionals of moving averages
• Point process and partial sum convergence for weakly dependent random variables with infinite variance
• On the Strong Mixing Property for Linear Sequences
• Non-central limit theorems for non-linear functional of Gaussian fields

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