Wavelet Methods in Statistics with R

Front Cover
Springer Science & Business Media, Aug 11, 2008 - Business & Economics - 257 pages
1 Review
Reviews aren't verified, but Google checks for and removes fake content when it's identified

Wavelet methods have recently undergone a rapid period of development with important implications for a number of disciplines including statistics. This book has three main objectives: (i) providing an introduction to wavelets and their uses in statistics; (ii) acting as a quick and broad reference to many developments in the area; (iii) interspersing R code that enables the reader to learn the methods, to carry out their own analyses, and further develop their own ideas. The book code is designed to work with the freeware R package WaveThresh4, but the book can be read independently of R.

The book introduces the wavelet transform by starting with the simple Haar wavelet transform, and then builds to consider more general wavelets, complex-valued wavelets, non-decimated transforms, multidimensional wavelets, multiple wavelets, wavelet packets, boundary handling, and initialization. Later chapters consider a variety of wavelet-based nonparametric regression methods for different noise models and designs including density estimation, hazard rate estimation, and inverse problems; the use of wavelets for stationary and non-stationary time series analysis; and how wavelets might be used for variance estimation and intensity estimation for non-Gaussian sequences.

The book is aimed both at Masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers/users interested in statistical wavelet methods.

Guy Nason is Professor of Statistics at the University of Bristol. He has been actively involved in the development of various wavelet methods in statistics since 1993. He was awarded the Royal Statistical Society’s 2001 Guy Medal in Bronze for work on wavelets in statistics. He was the author of the first, free, generally available wavelet package for statistical purposes in S and R (WaveThresh2).

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
12 Why Use Wavelets?
2
13 Why Wavelets in Statistics?
11
14 Software and This Book
13
Wavelets
15
22 Haar Wavelets on Functions
28
23 Multiresolution Analysis
37
24 Vanishing Moments
40
315 Block Thresholding
128
316 Miscellanea and Discussion
130
Related Wavelet Smoothing Techniques
133
43 NonGaussian Noise
138
44 Multidimensional Data
140
45 Irregularly Spaced Data
143
46 Confidence Bands
150
47 Density Estimation
155

25 WaveThresh Wavelets and What Some Look Like
41
26 Other Wavelets
45
27 The General Fast Discrete Wavelet Transform
50
28 Boundary Conditions
55
29 Nondecimated Wavelets
57
210 Multiple Wavelets
66
211 Wavelet Packet Transforms
68
212 Nondecimated Wavelet Packet Transforms
75
213 Multivariate Wavelet Transforms
76
214 Other Topics
78
Wavelet Shrinkage
83
32 Wavelet Shrinkage
84
33 The Oracle
85
34 Test Functions
88
36 Primary Resolution
96
38 Crossvalidation
98
39 False Discovery Rate
100
310 Bayesian Wavelet Shrinkage
101
312 NonDecimated Wavelet Shrinkage
110
313 Multiple Wavelet Shrinkage Multiwavelets
118
314 Complexvalued Wavelet Shrinkage
120
48 Survival Function Estimation
158
49 Inverse Problems
163
Multiscale Time Series Analysis
167
52 Stationary Time Series
169
53 Locally Stationary Time Series
174
54 Forecasting with Locally Stationary Wavelet Models
192
55 Time Series with Wavelet Packets
197
56 Related Topics and Discussion
198
Multiscale Variance Stabilization
201
61 Why the Square Root for Poisson?
202
62 The Fisz Transform
203
63 Poisson Intensity Function Estimation
206
64 The HaarFisz Transform for Poisson Data
207
65 Datadriven HaarFisz
217
66 Discussion
227
R Software for Wavelets and Statistics
229
Notation and Some Mathematical Concepts
231
Survival Function Code
235
References
237
Index
253
Copyright

Other editions - View all

Common terms and phrases