Bootstrap Techniques for Signal Processing

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Cambridge University Press, May 6, 2004 - Technology & Engineering
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The statistical bootstrap is one of the methods that can be used to calculate estimates of a certain number of unknown parameters of a random process or a signal observed in noise, based on a random sample. Such situations are common in signal processing and the bootstrap is especially useful when only a small sample is available or an analytical analysis is too cumbersome or even impossible. This book covers the foundations of the bootstrap, its properties, its strengths and its limitations. The authors focus on bootstrap signal detection in Gaussian and non-Gaussian interference as well as bootstrap model selection. The theory developed in the book is supported by a number of useful practical examples written in MATLAB. The book is aimed at graduate students and engineers, and includes applications to real-world problems in areas such as radar and sonar, biomedical engineering and automotive engineering.
 

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Contents

Introduction
1
The bootstrap principle
11
211 Some theoretical results for the mean
17
212 Examples of nonparametric bootstrap estimation
19
213 The parametric bootstrap
26
214 Bootstrap resampling for dependent data
28
215 Examples of dependent data bootstrap estimation
33
22 The principle of pivoting and variance stabilisation
49
45 Order selection in autoregressions
117
46 Detection of sources using bootstrap techniques
119
461 Bootstrap based detection
121
462 Null distribution estimation
124
463 Bias correction
126
464 Simulations
127
Real data bootstrap applications
130
511 Motivation
131

221 Some examples
51
23 Limitations of the bootstrap
57
24 Trends in bootstrap resampling
59
25 Summary
60
Signal detection with the bootstrap
62
311 Suboptimal detection
72
32 Hypothesis testing with the bootstrap
73
33 The role of pivoting
74
34 Variance estimation
78
35 Detection through regression
83
36 The bootstrap matched filter
93
361 Tolerance interval bootstrap matched filter
99
37 Summary
101
Bootstrap model selection
103
42 Model selection
105
43 Model selection in linear models
106
431 Model selection based on prediction
107
432 Bootstrap based model selection
108
433 A consistent bootstrap method
109
434 Dependent data in linear models
114
442 Use of bootstrap in model selection
115
513 Bootstrap tests
134
514 The experiment
135
52 Confidence intervals for aircraft parameters
136
522 Results with real passive acoustic data
139
53 Landmine detection
143
54 Noise floor estimation in overthehorizon radar
147
541 Principle of the trimmed mean
148
542 Optimal trimming
150
543 Noise floor estimation
151
55 Model order selection for corneal elevation
154
56 Summary
158
MATLAB codes for the examples
159
A12 The parametric bootstrap
160
A14 The principle of pivoting and variance stabilisation
161
A15 Limitations of bootstrap procedure
163
A17 The bootstrap matched filter
167
A19 Noise floor estimation
170
Bootstrap MATLAB Toolbox
174
References
201
Index
215
Copyright

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About the author (2004)

Abdelhak M. Zoubir received the Dipl.-Ing degree (BSc/BEng) from Fachhochschule Niederrhein, Germany, in 1983, the Dipl.-Ing. (MSc/MEng) and the Dr.-Ing. (PhD) degree from Ruhr University Bochum, Germany, in 1987 and 1992, all in Electrical Engineering. Early placement in industry (Klöckner-Moeller and Siempelkamp AG) was then followed by Associate Lectureship in the Division for Signal Theory at Ruhr University Bochum, Germany. In June 1992, he joined Queensland University of Technology where he was Lecturer, Senior Lecturer and then Associate Professor in the School of Electrical and Electronic Systems Engineering. In March 1999, he took up the position of Professor of Telecommunications at Curtin University of Technology, where he was Head of the School of Electrical & Computer Engineering from November 2001 until February 2003. In February 2003 he took up the position of Professor in Signal Processing at Darmstadt University of Technology. Dr Zoubir's general research interest lies in statistical methods for signal processing with applications in communications, sonar, radar, biomedical engineering and vibration analysis. His current research interest lies in robust estimation and in bootstrap techniques for spectrum estimation and the modelling of non-stationary and non-Gaussian signals. He was the General Co-Chairman of the Third IEEE International Symposium on Signal Processing and Information Technology (ISSPIT) held in Darmstadt in December 2003, the Technical Chairman of the 11th IEEE Workshop on Statistical Signal processing held in Singapore in August 2001 and Deputy Technical Chairman (Special Sessions/Tutorials) of ICASSP-94 held in Adelaide. He served as an Associate Editor of the IEEE Transactions on Signal Processing from 1999 until 2005 and is currently Associate Editor of the EURASIP journals Signal Processing and the Journal of Applied Signal Processing. Dr Zoubir is a Member of the IEEE SPS Technical Committees on Signal Processing Theory and M

D. Robert Iskander received his Ph.D. from Queensland University of Technology. He is currently a senior lecturer in the School of Engineering at Griffith University, Australia. He is also a visiting research fellow in the Centre for Eye Research at Queensland University of Technology. He has published over 50 technical papers, in fields such as statistical signal processing, visual optics, and ophthalmic instrumentation.

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