## Bootstrap Techniques for Signal ProcessingThe 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 |

215 | |

### Other editions - View all

Bootstrap Techniques for Signal Processing Abdelhak M. Zoubir,D. Robert Iskander Limited preview - 2004 |

Bootstrap Techniques for Signal Processing Abdelhak M. Zoubir,D. Robert Iskander No preview available - 2007 |

### Common terms and phrases

applications approximate asymptotic autoregressive block of blocks bootstrap based bootstrap estimates bootstrap matched filter bootstrap methods bootstrap model bootstrap procedure bootstrap resampling bootstrap statistics bootstrap techniques bootstrap test calculate CFAR Chapter circular block bootstrap Compute confidence bands confidence interval confidence interval estimation dependent data detector Efron and Tibshirani eigenvalues estimating the variance example false alarm frequency Gaussian distribution given hypothesis testing interval estimation jackknife large number least squares level of significance MATLAB MATLAB code matrix model selection nested bootstrap noise floor Noise floor estimation non-Gaussian non-parametric bootstrap null hypothesis number of bootstrap observations obtain output over-the-horizon radar parameter estimates parametric bootstrap periodogram polynomial problem random sample regression Repeat Steps resampling procedure sample eigenvalues sample mean sensor signal detection signal processing spectral density standard deviation target test statistic tolerance interval trimmed mean values Variance estimation variance stabilising transformation Zoubir