| Permutation and bootstrap statistics under infinite variance | p. 1 |
| Introduction | p. 1 |
| Some general sampling theorems | p. 2 |
| Application to change point detection | p. 10 |
| References | p. 19 |
| Max-Stable Processes: Representations, Ergodic Properties and Statistical Applications | p. 21 |
| Introduction | p. 21 |
| Representations of Max-Stable Processes | p. 24 |
| Ergodic Properties of Stationary Max-stable Processes | p. 29 |
| Examples and Statistical Applications | p. 32 |
| Ergodic Properties of Some Max-Stable Processes | p. 32 |
| Estimation of the Extremal Index | p. 35 |
| References | p. 40 |
| Best attainable rates of convergence for the estimation of the memory parameter | p. 43 |
| Introduction | p. 43 |
| Lower bound | p. 45 |
| Upper bound | p. 47 |
| Bandwidth selection | p. 49 |
| Technical results | p. 51 |
| References | p. 56 |
| Harmonic analysis tools for statistical inference in the spectral domain | p. 59 |
| Introduction | p. 59 |
| Motivation | p. 61 |
| Main result | p. 64 |
| Applications and discussion | p. 67 |
| References | p. 70 |
| On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time | p. 71 |
| Motivation | p. 72 |
| Infinitely divisible processes | p. 74 |
| Infinitely divisible cascade | p. 74 |
| Infinitely divisible motion | p. 76 |
| Fractional Brownian motion in multifractal time | p. 78 |
| Multiresolution quantities and scaling parameter estimation | p. 78 |
| Multiresolution quantities | p. 78 |
| Scaling parameter estimation procedures | p. 80 |
| Dependence structures of the multiresolution coefficients: analytical study | p. 80 |
| Correlation structures for increment and wavelet coefficients | p. 81 |
| Higher order correlations for increments | p. 83 |
| Role of the order of the increments | p. 85 |
| Dependence structures of the multiresolution coefficients: Conjectures and numerical studies | p. 85 |
| Conjectures | p. 85 |
| Numerical simulations | p. 86 |
| Discussions and conclusions on the role of the number of vanishing moments: | p. 89 |
| Proofs | p. 90 |
| A key lemma | p. 90 |
| Proof of Theorem 4.1 | p. 91 |
| Proof of Theorem 4.2 | p. 93 |
| Proof of Proposition 0.6 | p. 94 |
| Proof of Proposition 0.7 | p. 95 |
| Proof of Proposition 0.8 | p. 99 |
| References | p. 99 |
| Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes | p. 103 |
| Introduction | p. 103 |
| Multifractal products of stochastic processes | p. 104 |
| Geometric Ornstein-Uhlenbeck processes | p. 108 |
| Multifractal Ornstein-Uhlenbeck processes | p. 113 |
| Log-tempered stable scenario | p. 113 |
| Log-normal tempered stable scenario | p. 116 |
| References | p. 120 |
| A new look at measuring dependence | p. 123 |
| Introduction | p. 123 |
| Bivariate dependence | p. 125 |
| Global dependence measures | p. 126 |
| Local dependence measures | p. 130 |
| Connections with reliability theory | p. 133 |
| Multivariate dependence | p. 135 |
| Moment inequalities and limit theorems | p. 137 |
| References | p. 139 |
| Robust regression with infinite moving average errors | p. 143 |
| Introduction | p. 143 |
| S-estimators | p. 144 |
| S-estimators' Asymptotic Behavior | p. 145 |
| Weak Convergence of estimators | p. 146 |
| Proof of Proposition 1 | p. 150 |
| Discussion | p. 156 |
| References | p. 156 |
| A note on the monitoring of changes in linear models with dependent errors | p. 159 |
| Introduction | p. 159 |
| The testing procedure | p. 160 |
| Examples | p. 163 |
| Linear models with NED regressors | p. 163 |
| Linear models with asymptotically M-dependent errors | p. 164 |
| Monitoring strongly mixing AR models | p. 165 |
| Proofs | p. 167 |
| References | p. 173 |
| Testing for homogeneity of variance in the wavelet domain | p. 175 |
| Introduction | p. 176 |
| The wavelet transform of K-th order difference stationary processes | p. 178 |
| Asymptotic distribution of the W2-CUSUM statistics | p. 180 |
| The single-scale case | p. 180 |
| The multiple-scale case | p. 187 |
| Test statistics | p. 190 |
| Power of the W2-CUSUM statistics | p. 192 |
| Power of the test in single scale case | p. 192 |
| Power of the test in multiple scales case | p. 196 |
| Some examples | p. 198 |
| References | p. 204 |
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