Essential Wavelets for Statistical Applications and Data Analysis R.T. Ogden, University of South Carolina 0-8176-3864-4 * 1996 * $40.00 * Hardcover * 285 pages * 40 Illustrations

1. Why Wavelets?
   1.1 What are wavelets used for?
2. Wavelets: A Brief Introduction
   2.1 The discrete Fourier transform
   2.2 The Haar system
   2.2.1 Multiresolution analysis
   2.2.2 The wavelet representation
   2.2.3 Goals of multiresolution analysis
   2.3 Smoother wavelet bases
3. Basic Smoothing Techniques
   3.1 Density estimation
   3.1.1 Histograms
   3.1.2 Kernel estimation
   3.1.3 Orthogonal series estimation
   3.2 Estimation of a regression function
   3.2.1 Kernel regression
   3.2.2 Orthogonal series estimation
   3.3 Kernel representation of orthogonal series estimators
4. Elementary Statistical Application
   4.1 Density estimation
   4.1.1 Haar-based histograms
   4.1.2 Estimation with smoother wavelets
   4.2 Nonparametric regression
5. Wavelet Features and Examples
   5.1 Wavelet decomposition and reconstruction
   5.1.1 Two-scale relationships
   5.1.2 The decomposition algorithm
   5.1.3 The reconstruction algorithm
   5.2 The filter representation
   5.3 Time-frequency localization
   5.3.1 The continuous Fourier transform
   5.3.2 The windowed Fourier transform
   5.3.3 The continuous wavelet transform
   5.4 Examples of wavelets and their constructions
   5.4.1 Orthogonal wavelets
   5.4.2 Biorthogonal wavelets
   5.4.3 Semiorthogonal wavelets
6. Wavelet-based Diagnostics
   6.1 Multiresolution plots
   6.2 Time-scale plots
   6.3 Plotting wavelet coefficients
   6.4 Other plots for data analysis
7. Some Practical Issues
   7.1 The discrete Fourier transform of data
   7.1.1 The Fourier transform of sampled signals
   7.1.2 The fast Fourier transform
   7.2 The wavelet transform of data
   7.3 Wavelets on an interval
   7.3.1 Periodic boundary handling
   7.3.2 Symmetric and antisymmetric boundary handling
   7.3.3 Meyer boundary waveless
   7.3.4 Orthogonal waveless on the interval
   7.4 When the sample size is not a power of two
8. Other Applications
   8.1 Selective wavelet reconstruction
   8.1.1 Wavelet thresholding
   8.1.2 Spatial adaptivity
   8.1.3 Global thresholding
   8.1.4 Estimation of the noise level
   8.2 More density estimation
   8.3 Spectral density estimation
   8.4 Detections of jumps and cusps
9. Data Adaptive Wavelet Thresholding
   9.1 SURE Thresholding
   9.2 Threshold selection by hypothesis testing
   9.2.1 Recursive testing
   9.2.2 Minimizing false discovery
   9.3 Cross-validation methods
   9.4 Bayesian methods
10. Generalizations and Extensions
    10.1 Two-dimensional wavelets
    10.2 Wavelet packets
    10.2.1 Wavelet packet functions
    10.2.2 The best basis algorithm
    10.3 Translation invariant wavelet smoothing

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