Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

By Anestis Antoniadis, Jérémie Bigot, Theofanis Sapatinas. 2001

394 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/1e93d7b303abf70d41372e93e4a9e58d85409531

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Citations in the corpus

Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes (2003, background): “For comprehensive expositions and reviews on wavelets in statistical settings we refer, for example, to [1,5,6,43].”
Bayesian fMRI data analysis with sparse spatial basis function priors (2007, methodology): “The sparsity property of the wavelet transform has been extensively applied for denoising with wavelet shrinkage (Donoho and Johnstone, 1994, 1995; Clyde et al., 1998; Antoniadis et al., 2001).”
Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators (2006, background): “Most of them are described in detailed in [45] and [4].”
Forecasting East Asian Indices Futures via a Novel Hybrid of Wavelet-PCA Denoising and Artificial Neural Network Models (2016, methodology): “Although Daubechies and Symlets use future data for transformations, causing boundary problems, we overcome this effect by time adjustments in the evaluation part.”
Wavelet-based motion artifact removal for functional near-infrared spectroscopy (2012, methodology): “Our model is similar to the one described by Antoniadis et al (2001) with the assumption that only coefficients from normal distribution with smaller variance in the mixture model belong to the original signal.”
Adaptive density estimation: a curse of support? ✩ (2009, background): “ual transformation (see Brown et al. (2007)). So basically the thresholding rules adapted to the Gaussian regression setting should work here (we refer the reader to the very complete review paper of Antoniadis et al. (2001) which provides descriptions and comparisons of various wavelet shrinkage an”
Wavelets and their applications (2007, methodology): “This latter point can be usefully supplemented by two more recent articles: [ANT 97] and [ANT 01].”
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, methodology): “Our wavelet-domain detection is formulated by hypothesis tests [35], i.”
Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding (2009, methodology): “Apart from the standard wavelet thresholding described above, a number of modifications are investigated in Section V, including translation invariant thresholding [14] and Bayesian-based wavelet thresholding [15], [18].”
Grouped variable importance with random forests and application to multiple functional data analysis (2014, methodology): “The wavelet transform is widely used in signal processing and for non parametric function estimation (see for instance Antoniadis et al.; 2001).”