Bootstrap Techniques for Signal Processing

by Abdelhak M. Zoubir , D. Robert Iskander

• ISBN13: 9780521034050
• ISBN10: 0521034051
• Format: Paperback
• Copyright: 2007-02-26
• Publisher: Cambridge University Press

Summary

A signal processing practitioner often asks themselves, "How accurate is my parameter estimator?" There may be no answer to this question if an analytic analysis is too cumbersome and the measurements sample is too small. The statistical bootstrap, an elegant solution, re-uses the original data with a computer to re-estimate the parameters and infer their accuracy.

Author Biography

D. Robert Iskander is currently a senior lecturer in the School of Engineering at Griffith University, Australia.

Table of Contents

Preface	p. ix
Notations	p. xii
Introduction	p. 1
The bootstrap principle	p. 11
The principle of resampling	p. 11
Some theoretical results for the mean	p. 17
Examples of non-parametric bootstrap estimation	p. 19
The parametric bootstrap	p. 26
Bootstrap resampling for dependent data	p. 28
Examples of dependent data bootstrap estimation	p. 33
The principle of pivoting and variance stabilisation	p. 49
Some examples	p. 51
Limitations of the bootstrap	p. 57
Trends in bootstrap resampling	p. 59
Summary	p. 60
Signal detection with the bootstrap	p. 62
Principles of hypothesis testing	p. 62
Sub-optimal detection	p. 72
Hypothesis testing with the bootstrap	p. 73
The role of pivoting	p. 74
Variance estimation	p. 78
Detection through regression	p. 83
The bootstrap matched filter	p. 93
Tolerance interval bootstrap matched filter	p. 99
Summary	p. 101
Bootstrap model selection	p. 103
Preliminaries	p. 103
Model selection	p. 105
Model selection in linear models	p. 106
Model selection based on prediction	p. 107
Bootstrap based model selection	p. 108
A consistent bootstrap method	p. 109
Dependent data in linear models	p. 114
Model selection in nonlinear models	p. 114
Data model	p. 114
Use of bootstrap in model selection	p. 115
Order selection in autoregressions	p. 117
Detection of sources using bootstrap techniques	p. 119
Bootstrap based detection	p. 121
Null distribution estimation	p. 124
Bias correction	p. 126
Simulations	p. 127
Summary	p. 127
Real data bootstrap applications	p. 130
Optimal sensor placement for knock detection	p. 130
Motivation	p. 131
Data model	p. 131
Bootstrap tests	p. 134
The experiment	p. 135
Confidence intervals for aircraft parameters	p. 136
Introduction	p. 136
Results with real passive acoustic data	p. 139
Landmine detection	p. 143
Noise floor estimation in over-the-horizon radar	p. 147
Principle of the trimmed mean	p. 148
Optimal trimming	p. 150
Noise floor estimation	p. 151
Model order selection for corneal elevation	p. 154
Summary	p. 158
Matlab codes for the examples	p. 159
Basic non-parametric bootstrap estimation	p. 159
The parametric bootstrap	p. 160
Bootstrap resampling for dependent data	p. 160
The principle of pivoting and variance stabilisation	p. 161
Limitations of bootstrap procedure	p. 163
Hypothesis testing	p. 163
The bootstrap matched filter	p. 167
Bootstrap model selection	p. 167
Noise floor estimation	p. 170
Bootstrap Matlab Toolbox	p. 174
References	p. 201
Index	p. 215
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