1 Wavelets: A Brief Introduction. - 1. 1 The Discrete Fourier Transform. - 1. 2 The Haar System. - Multiresolution Analysis. - The Wavelet Representation. - Goals of Multiresolution Analysis. - 1. 3 Smoother Wavelet Bases. - 2 Basic Smoothing Techniques. - 2. 1 Density Estimation. - Histograms. - Kernel Estimation. - Orthogonal Series Estimation. - 2. 2 Estimation of a Regression Function. - Kernel Regression. - Orthogonal Series Estimation. - 2. 3 Kernel Representation of Orthogonal Series Estimators. - 3 Elementary Statistical Applications. - 3. 1 Density Estimation. - Haar-Based Histograms. - Estimation with Smoother Wavelets. - 3. 2 Nonparametric Regression. - 4 Wavelet Features and Examples. - 4. 1 Wavelet Decomposition and Reconstruction. - Two-Scale Relationships. - The Decomposition Algorithm. - The Reconstruction Algorithm. - 4. 2 The Filter Representation. - 4. 3 Time-Frequency Localization. - The Continuous Fourier Transform. - The Windowed Fourier Transform. - The Continuous Wavelet Transform. - 4. 4 Examples of Wavelets and Their Constructions. - Orthogonal Wavelets. - Biorthogonal Wavelets. - Semiorthogonal Wavelets. - 5 Wavelet-based Diagnostics. - 5. 1 Multiresolution Plots. - 5. 2 Time-Scale Plots. - 5. 3 Plotting Wavelet Coefficients. - 5. 4 Other Plots for Data Analysis. - 6 Some Practical Issues. - 6. 1 The Discrete Fourier Transform of Data. - The Fourier Transform of Sampled Signals. - The Fast Fourier Transform. - 6. 2 The Wavelet Transform of Data. - 6. 3 Wavelets on an Interval. - Periodic Boundary Handling. - Symmetric and Antisymmetric Boundary Handling. - Meyer Boundary Wavelets. - Orthogonal Wavelets on the Interval. - 6. 4 When the Sample Size is Not a Power of Two. - 7 Other Applications. - 7. 1 Selective Wavelet Reconstruction. - Wavelet Thresholding. - Spatial Adaptivity. - Global Thresholding. - Estimation of the Noise Level. - 7. 2 More Density Estimation. - 7. 3 Spectral Density Estimation. - 7. 4 Detections of Jumps and Cusps. - 8 Data Adaptive Wavelet Thresholding. - 8. 1 SURE Thresholding. - 8. 2 Threshold Selection by Hypothesis Testing. - Recursive Testing. - Minimizing False Discovery. - 8. 3 Cross-Validation Methods. - 8. 4 Bayesian Methods. - 9 Generalizations and Extensions. - 9. 1 Two-Dimensional Wavelets. - 9. 2 Wavelet Packets. - Wavelet Packet Functions. - The Best Basis Algorithm. - 9. 3 Translation Invariant Wavelet Smoothing. - References. - Glossary of Notation. - Glossary of Terms. Language: English