A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence

Ein allgemeines Resultat über den mittleren integrierten quadratischen Fehler des Hard-Thresholding-Wavelet-Schätzers unter α-mischender Abhängigkeit

Clicks: 391
ID: 69912
2014
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Abstract
We consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.
Wir betrachten die Schätzung einer unbekannten Funktion f für schwach abhängige Daten (α-mischend) in einem allgemeinen Rahmen. Unser Beitrag ist theoretischer Natur: Wir beweisen, dass ein Hard-Thresholding-Wavelet-Schätzer eine scharfe Konvergenzrate bezüglich des mittleren integrierten quadratischen Fehlers (MISE) über Besov-Kugeln erreicht, ohne allzu restriktive Annahmen an das Modell zu stellen. Anwendungen werden für zwei Arten inverser Probleme vorgestellt: die Dekonvolutions-Dichteschätzung und die Dichteschätzung in einem Modell vom GARCH-Typ; beide verbessern bestehende Resultate in diesem abhängigen Kontext. Eine weitere Anwendung betrifft das Regressionsmodell mit zufälligem Design.
Reference Key
chesneau2014ajournal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Chesneau, Christophe;
Journal journal of probability and statistics
Year 2014
DOI
DOI not found
URL
http://dx.doi.org/10.1155/2014/403764
Keywords
Biology (General) economics as a science agriculture probabilities. mathematical statistics

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