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Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study. Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced.


References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Shirazi, Esmaeil; Chaubey, Yogendra P.; Doosti, Hassan; Nirumand, Hossein Ali: Wavelet based estimation for the derivative of a density by block thresholding under random censorship (2012)
  2. Autin, Florent; Freyermuth, Jean-Marc; von Sachs, Rainer: Ideal denoising within a family of tree-structured wavelet estimators (2011)
  3. Petsa, Athanasia; Sapatinas, Theofanis: On the estimation of the function and its derivatives in nonparametric regression: a Bayesian testimation approach (2011)
  4. Chesneau, C.; Fadili, J.; Starck, J.-L.: Stein block thresholding for image denoising (2010)
  5. Pensky, Marianna; Sapatinas, Theofanis: On convergence rates equivalency and sampling strategies in functional deconvolution models (2010)
  6. Serban, Nicoleta: Noise reduction for enhanced component identification in multi-dimensional biomolecular NMR studies (2010)
  7. Abramovich, Felix; De Feis, Italia; Sapatinas, Theofanis: Optimal testing for additivity in multiple nonparametric regression (2009)
  8. Cutillo, Luisa; Jung, Yoon Young; Ruggeri, Fabrizio; Vidakovic, Brani: Larger posterior mode wavelet thresholding and applications (2008)
  9. Lavielle, Marc; Ludeña, Carenne: Random thresholds for linear model selection (2008)
  10. Abramovich, Felix; Angelini, Claudia; De Canditiis, Daniela: Pointwise optimality of Bayesian wavelet estimators (2007)
  11. Aminghafari, Mina; Cheze, Nathalie; Poggi, Jean-Michel: Multivariate denoising using wavelets and principal component analysis (2006)
  12. Katul, Gabriel; Ruggeri, Fabrizio; Vidakovic, Brani: Denoising ozone concentration measurements with bams filtering (2006)
  13. Bigot, Jérémie: A scale-space approach with wavelets to singularity estimation (2005)
  14. Comte, F.; Rozenholc, Y.: A new algorithm for fixed design regression and denoising (2004)
  15. Antoniadis, Anestis; Sapatinas, Theofanis: Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes (2003)
  16. Anestis Antoniadis; Jeremie Bigot; Theofanis Sapatinas: Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study (2001) not zbMATH