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. Taleb, Youssef; Cohen, Edward A. K.: Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation (2021)
  2. Amato, Umberto; Antoniadis, Anestis; De Feis, Italia: Flexible, boundary adapted, nonparametric methods for the estimation of univariate piecewise-smooth functions (2020)
  3. Aston, John; Autin, Florent; Claeskens, Gerda; Freyermuth, Jean-Marc; Pouet, Christophe: Minimax optimal procedures for testing the structure of multidimensional functions (2019)
  4. Yu, Dengdeng; Zhang, Li; Mizera, Ivan; Jiang, Bei; Kong, Linglong: Sparse wavelet estimation in quantile regression with multiple functional predictors (2019)
  5. Hassanein, Maha A.; Hanna, Magdy Tawfik; Seif, Nabila Philip Attalla; Elbarawy, Menna T. M. M.: Signal denoising using optimized trimmed thresholding (2018)
  6. Naulet, Zacharie; Barat, Éric: Some aspects of symmetric Gamma process mixtures (2018)
  7. Navarro, Fabien; Saumard, Adrien: Slope heuristics and V-fold model selection in heteroscedastic regression using strongly localized bases (2017)
  8. Sanyal, Nilotpal; Ferreira, Marco A. R.: Bayesian wavelet analysis using nonlocal priors with an application to fMRI analysis (2017)
  9. Ali, Syed Twareque: Reproducing kernels in coherent states, wavelets, and quantization (2015)
  10. Antoniadis, A.; Glad, I. K.; Mohammed, H.: Local comparison of empirical distributions via nonparametric regression (2015)
  11. Autin, Florent; Claeskens, Gerda; Freyermuth, Jean-Marc: Asymptotic performance of projection estimators in standard and hyperbolic wavelet bases (2015)
  12. Gregorutti, Baptiste; Michel, Bertrand; Saint-Pierre, Philippe: Grouped variable importance with random forests and application to multiple functional data analysis (2015)
  13. Shokripour, Mona; Aminghafari, Mina: Wavelet-based estimation for multivariate stable laws (2015)
  14. De Canditiis, Daniela: A frame based shrinkage procedure for fast oscillating functions (2014)
  15. Haltmeier, Markus; Munk, Axel: Extreme value analysis of empirical frame coefficients and implications for denoising by soft-thresholding (2014)
  16. Lacaux, Céline; Muller-Gueudin, Aurélie; Ranta, Radu; Tindel, Samy: Convergence and performance of the peeling wavelet denoising algorithm (2014)
  17. Om, Hari; Biswas, Mantosh: An adaptive image denoising method based on local parameters optimization (2014)
  18. Bigot, Jérémie: Fréchet means of curves for signal averaging and application to ECG data analysis (2013)
  19. Reményi, Norbert; Vidakovic, Brani: (\Lambda)-neighborhood wavelet shrinkage (2013)
  20. Lee, Kichun; Vidakovic, Brani: Semi-supervised wavelet shrinkage (2012)

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