Some laws of the iterated logarithm in Hilbertian autoregressive models

DOI10.1016/j.jmva.2003.07.001zbMath1142.60323OpenAlexW2033258956MaRDI QIDQ1765623

Ludovic Menneteau

Publication date: 23 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jmva.2003.07.001

zbMATH Keywords

Functional principal component analysisAutoregressive Hilbertian processesCovariance operatorsLaws of the iterated logarithm

Mathematics Subject Classification ID

Strong limit theorems (60F15) Inference from stochastic processes (62M99) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (12)

Moderate deviation principle for autoregressive processes ⋮ Consistency of the plug-in functional predictor of the Ornstein-Uhlenbeck process in Hilbert and Banach spaces ⋮ The law of iterated logarithm for autoregressive processes ⋮ Large and moderate deviations for infinite-dimensional autoregressive processes. ⋮ A LIL for independent non-identically distributed random variables in Banach space and its applications ⋮ Asymptotic properties of a component-wise ARH(1) plug-in predictor ⋮ The Discounted Large Deviation Principle for Autoregressive Processes ⋮ Asymptotic normality of autoregressive processes ⋮ Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root ⋮ Weak convergence in the functional autoregressive model ⋮ Laws of the iterated logarithm and an almost sure invariance principle for mixing \(B\)-valued random variables and autoregressive processes ⋮ The Discounted Berry-Esséen Analogue for Autoregressive Processes

Uses Software

• fda (R)

Cites Work

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