Adaptive estimation for Weakly Dependent Functional Times Series

The local regularity of functional time series is studied under \(L^p-m-\)appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Maissoro, Hassan, Patilea, Valentin, Vimond, Myriam
Format: Article
Language:English
Subjects:
Asymptotic properties
Estimators
Normality
Regularity
Online Access:Get full text
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Summary:The local regularity of functional time series is studied under \(L^p-m-\)appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric mean and autocovariance functions estimators that adapt to the regularity and the design, which can be sparse or dense. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators.
ISSN:2331-8422