A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence. (19th January 2014)

• Record Type: Journal Article
• Authors: Chesneau, Christophe
• Other Names: Bai Zhidong Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2014(2014)
• Publication Date: 2014-01-19
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2014/403764
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : We consider the estimation of an unknown functionf 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.