Nonparametric estimation for functional data by wavelet thresholding

* This paper deals with density and regression estimation problems for functional data. Using wavelet bases for Hilbert spaces of functions, we develop a new adaptive procedure based on a term-by-term selection of the wavelet coefficients estimators. We study its asymptotic performances by consideri...

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Bibliographic Details
Published inRevstat Vol. 11; no. 2; pp. 211 - 230
Main Authors Chesneau, Christophe, Kachour, Maher, Maillot, Bertrand
Format Journal Article
LanguageEnglish
Published Instituto Nacional de Estatistica 01.06.2013
Subjects
Coefficients
Hilbert space
Mathematical research
Mathematics
Regression analysis
Statistics
Statistics Theory
Wavelet transforms
Density estimation
Wavelets
Functional data
Hard thresholding
Nonparametric regression
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Summary:* This paper deals with density and regression estimation problems for functional data. Using wavelet bases for Hilbert spaces of functions, we develop a new adaptive procedure based on a term-by-term selection of the wavelet coefficients estimators. We study its asymptotic performances by considering the mean integrated squared error over adapted decomposition spaces. Key-Words: * functional data; density estimation; nonparametric regression; wavelets; hard thresholding. AMS Subject Classification: * 62G07, 60B11.
ISSN:1645-6726