Dependence in Probability and Statistics (eBook)

Paul Doukhan, Gabriel Lang, Donatas Surgailis, Gilles Teyssière (Herausgeber)

eBook Download: PDF

2010
XV, 205 Seiten
Springer Berlin (Verlag)
978-3-642-14104-1 (ISBN)

Infos

This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.

Inhalt

Preface 6
Contents 10
List of Contributors 14
Permutation and bootstrap statistics underinfinite variance 18
1 Introduction 18
2 Some general sampling theorems 19
3 Application to change point detection 27
References 36
Max–Stable Processes: Representations, Ergodic Properties and Statistical Applications 38
1 Introduction 38
2 Representations of Max–Stable Processes 41
3 Ergodic Properties of Stationary Max–stable Processes 46
4 Examples and Statistical Applications 49
4.1 Ergodic Properties of Some Max–Stable Processes 49
4.2 Estimation of the Extremal Index 52
References 57
Best attainable rates of convergence for the estimation of the memory parameter 60
1 Introduction 60
2 Lower bound 62
3 Upper bound 64
4 Bandwidth selection 66
5 Technical results 68
References 73
Harmonic analysis tools for statistical inference in the spectral domain 75
1 Introduction 75
2 Motivation 77
3 Main result 80
4 Applications and discussion 83
References 86
On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time 87
1 Motivation 88
2 Infinitely divisible processes 90
2.1 Infinitely divisible cascade 90
2.2 Infinitely divisible motion 92
2.3 Fractional Brownian motion in multifractal time 94
3 Multiresolution quantities and scaling parameter estimation 94
3.1 Multiresolution quantities 94
3.2 Scaling parameter estimation procedures 96
4 Dependence structures of the multiresolution coefficients: analytical study 96
4.1 Correlation structures for increment and wavelet coefficients 97
4.1.1 Increments 97
4.1.2 Wavelet coefficients 97
4.1.3 Vanishing moments and correlation 98
4.2 Higher order correlations for increments 99
4.2.1 First order increments 99
4.2.2 Second order increments 100
4.3 Role of the order of the increments 101
5 Dependence structures of the multiresolution coefficients: Conjectures and numerical studies 101
5.1 Conjectures 101
5.2 Numerical simulations 102
5.2.1 Simulation set up 102
5.2.2 Goal and analysis 103
5.2.3 Results and analyses 103
6 Discussions and conclusions on the role of the number of vanishing moments: 105
7 Proofs 106
7.1 A key lemma 106
7.2 Proof of Theorem 4.1 107
7.3 Proof of Theorem 4.2 109
7.4 Proof of Proposition 0.6 110
7.5 Proof of Proposition 0.7 111
7.6 Proof of Proposition 0.8 115
References 115
Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes 118
1 Introduction 118
2 Multifractal products of stochastic processes 119
3 Geometric Ornstein-Uhlenbeck processes 123
4 Multifractal Ornstein-Uhlenbeck processes 128
4.1 Log-tempered stable scenario 128
4.2 Log-normal tempered stable scenario 131
References 135
A new look at measuring dependence 138
1 Introduction 138
2 Bivariate dependence 140
2.1 Global dependence measures 141
2.2 Local dependence measures 145
3 Connections with reliability theory 148
4 Multivariate dependence 150
5 Moment inequalities and limit theorems 152
References 154
Robust regression with infinite moving average errors 158
1 Introduction 158
2 S-estimators 159
3 S-estimators’ Asymptotic Behavior 160
3.1 Weak Convergence of estimators 161
4 Proof of Proposition 1 165
5 Discussion 171
References 171
A note on the monitoring of changes in linear models with dependent errors 173
1 Introduction 173
2 The testing procedure 174
3 Examples 177
3.1 Linear models with NED regressors 177
3.2 Linear models with asymptotically M-dependent errors 178
3.3 Monitoring strongly mixing AR models 179
4 Proofs 181
References 187
Testing for homogeneity of variance in the wavelet domain. 189
1 Introduction 190
2 The wavelet transform of K-th order difference stationary processes 192
3 Asymptotic distribution of the W2-CUSUM statistics 194
3.1 The single-scale case 194
3.2 The multiple-scale case 201
4 Test statistics 204
5 Power of the W2-CUSUM statistics 206
5.1 Power of the test in single scale case 206
5.2 Power of the test in multiple scales case 210
6 Some examples 212
6.0.1 Asymptotic level of KSM and CVM. 213
6.0.2 Power of KSM and CVM. 215
6.0.3 Estimation of the change point in the original process. 216
References 218
Lecture Notes in Statistics 220

Produkt-Details

• Erscheint lt. Verlag: 23.7.2010
• Reihe/Serie: Lecture Notes in Statistics
• Reihe/Serie: Lecture Notes in Statistics
• Zusatzinfo: XV, 205 p. 13 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Bootstrap • change-point detection • Estimator • linear regression • Long Memory • measure • multifractality • Statistica • Wavelets • weak dependence
• ISBN-10: 3-642-14104-8 / 3642141048
• ISBN-13: 978-3-642-14104-1 / 9783642141041