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 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.
Author(s): Abdelhak M. Zoubir, D. Robert Iskander
Publisher: Cambridge University Press
Year: 2004
Language: English
Pages: 232
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
General notation......Page 14
Greek symbols......Page 15
Acronyms......Page 16
1 Introduction......Page 17
2.1 The principle of resampling......Page 27
2.1.1 Some theoretical results for the mean......Page 33
2.1.3 The parametric bootstrap......Page 42
2.1.4 Bootstrap resampling for dependent data......Page 44
2.2 The principle of pivoting and variance stabilisation......Page 65
2.2.1 Some examples......Page 67
2.3 Limitations of the bootstrap......Page 73
2.4 Trends in bootstrap resampling......Page 75
2.5 Summary......Page 76
3.1 Principles of hypothesis testing......Page 78
3.1.1 Sub-optimal detection......Page 88
3.2 Hypothesis testing with the bootstrap......Page 89
3.3 The role of pivoting......Page 90
3.4 Variance estimation......Page 94
3.5 Detection through regression......Page 99
3.6 The bootstrap matched filter......Page 109
3.6.1 Tolerance interval bootstrap matched filter......Page 115
3.7 Summary......Page 117
4.1 Preliminaries......Page 119
4.2 Model selection......Page 121
4.3 Model selection in linear models......Page 122
4.3.1 Model selection based on prediction......Page 123
4.3.2 Bootstrap based model selection......Page 124
4.3.3 A consistent bootstrap method......Page 125
4.4.1 Data model......Page 130
4.4.2 Use of bootstrap in model selection......Page 131
4.5 Order selection in autoregressions......Page 133
4.6 Detection of sources using bootstrap techniques......Page 135
4.6.1 Bootstrap based detection......Page 137
4.6.2 Null distribution estimation......Page 140
4.6.3 Bias correction......Page 142
4.7 Summary......Page 143
5.1 Optimal sensor placement for knock detection......Page 146
5.1.2 Data model......Page 147
5.1.3 Bootstrap tests......Page 150
5.1.4 The experiment......Page 151
5.2.1 Introduction......Page 152
5.2.2 Results with real passive acoustic data......Page 155
5.3 Landmine detection......Page 159
5.4 Noise floor estimation in over-the-horizon radar......Page 163
5.4.1 the Principle of trimmed mean......Page 164
5.4.2 Optimal trimming......Page 166
5.4.3 Noise floor estimation......Page 167
5.5 Model order selection for corneal elevation......Page 170
5.6 Summary......Page 174
A1.1 Basic non-parametric bootstrap estimation......Page 175
A1.3 Bootstrap resampling for dependent data......Page 176
A1.4 The principle of pivoting and variance stabilisation......Page 177
A1.6 Hypothesis testing......Page 179
A1.8 Bootstrap model selection......Page 183
A1.9 Noise floor estimation......Page 186
A2.1 Bootstrap Toolbox Contents......Page 190
References......Page 217
Index......Page 231
