Smooth hyperbolic wavelet deconvolution with anisotropic structure

Justin Wishart

Research output: Contribution to journalArticleResearchpeer-review

Abstract

This paper considers a deconvolution regression problem in a multivariate setting with anisotropic structure and constructs an estimator of the function of interest using the hyperbolic wavelet basis. The deconvolution structure assumed is an anisotropic version of the smooth type (either regular-smooth or super-smooth). The function of interest is assumed to belong to a Besov space with anisotropic smoothness. Global performances of the presented hyperbolic wavelet estimators is measured by obtaining upper bounds on convergence rates in the Lp-risk with 1≤p≤2 and 1≤p<∞ in the regular-smooth and super-smooth cases respectively. The results are compared and contrasted with existing convergence results in the literature.
LanguageEnglish
Pages1694-1716
Number of pages23
JournalElectronic Journal of Statistics
Volume13
Issue number1
DOIs
Publication statusPublished - 24 Apr 2019

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Deconvolution
Wavelets
Wavelet Estimator
Wavelet Bases
Besov Spaces
Convergence Results
Convergence Rate
Smoothness
Regression
Estimator
Upper bound
Convergence rate

Bibliographical note

Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

  • Besov spaces
  • Brownian sheet
  • deconvolution
  • Fourier analysis
  • hyperbolic wavelet analysis
  • anisotropic
  • nonparametric regression
  • Wavelets
  • Hyperbolic wavelet analysis
  • Deconvolution
  • Meyer wavelets
  • Anisotropic

Cite this

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Smooth hyperbolic wavelet deconvolution with anisotropic structure. / Wishart, Justin.

In: Electronic Journal of Statistics, Vol. 13, No. 1, 24.04.2019, p. 1694-1716.

Research output: Contribution to journalArticleResearchpeer-review

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