Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes

DOI10.1016/S0167-7152(01)00151-1zbMath0999.62068OpenAlexW2040732590MaRDI QIDQ1612934

Serge Guillas

Publication date: 5 September 2002

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(01)00151-1

zbMATH Keywords

rate of convergenceHilbert spaceautoregressive processesfunctional data

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Applications of functional analysis in probability theory and statistics (46N30)

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Boosting for real and functional samples: an application to an environmental problem ⋮ Consistency of the plug-in functional predictor of the Ornstein-Uhlenbeck process in Hilbert and Banach spaces ⋮ On the rate of convergence for the autocorrelation operator in functional autoregression ⋮ The Maximum of the Periodogram of a Sequence of Functional Data ⋮ Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data ⋮ A note on strong-consistency of componentwise ARH(1) predictors ⋮ Rates of convergence of autocorrelation estimates for periodically correlated autoregressive Hilbertian processes ⋮ Asymptotic properties of a component-wise ARH(1) plug-in predictor ⋮ Functional maximum-likelihood estimation of ARH(\(p\)) models ⋮ Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors ⋮ Kalman filtering from POP-based diagonalization of ARH(1) ⋮ Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics ⋮ Lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces ⋮ Estimation and simulation of autoregressive Hilbertian processes with exogenous variables

Cites Work

• Functional linear model
• Autoregressive Forecasting of Some Functional Climatic Variations
• Approximation spline de la prevision d'un processus fonctionnel autorégressif d'ordre 1
• Non-causalité et discrétisation fonctionnelle, théorèmes limites pour un processus
• A family of minimax rates for density estimators in continuous time
• Normalité asymptotique de l'estimateur empirique de l'opérateur d'autocorrélation d'un processus ARH(1)
• Ridge Regression: Biased Estimation for Nonorthogonal Problems
• Unnamed Item

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