Wavelet methods
Piotr Fryźlewicz · Wiley Interdisciplinary Reviews Computational Statistics · 2010
Abstract This overview article motivates the use of wavelets in statistics and introduces the basic mathematics behind the construction of wavelets. Topics covered include the continuous and discrete wavelet transforms, multiresolution analysis, and the non‐decimated wavelet transform. We describe the basic mechanics of nonparametric function estimation via wavelets, emphasizing the concepts of sparsity and thresholding. A simple proof of the mean‐square consistency of the wavelet estimator is also included. The article ends with two special topics: function estimation with unbalanced Haar wavelets and variance stabilization via the Haar–Fisz transformation.WIREs Comp Stat2010 2 654–667 DOI: 10.1002/wics.124 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Applications of Computational Statistics > Signal and Image Processing and Coding