Dependence in Probability and Statistics

1. Front Matter

   Pages i-xv

   PDF

2. Permutation and bootstrap statistics under infinite variance

   • István Berkes, Lajos Horváth, Johannes Schauer

   Pages 1-20

3. Max–Stable Processes: Representations, Ergodic Properties and Statistical Applications

   • Stilian A. Stoev

   Pages 21-42

4. Best attainable rates of convergence for the estimation of the memory parameter

   • Philippe Soulier

   Pages 43-57

5. Harmonic analysis tools for statistical inference in the spectral domain

   • Florin Avram, Nikolai Leonenko, Ludmila Sakhno

   Pages 59-70

6. On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time

   • Béatrice Vedel, Herwig Wendt, Patrice Abry, Stéphane Jaffard

   Pages 71-101

7. Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes

   • Vo V. Anh, Nikolai N. Leonenko, Narn-Rueih Shieh

   Pages 103-122

8. A new look at measuring dependence

   • Wei Biao Wu, Jan Mielniczuk

   Pages 123-142

9. Robust regression with infinite moving average errors

   • Patrick J. Farrell, Mohamedou Ould-Haye

   Pages 143-157

10. A note on the monitoring of changes in linear models with dependent errors

    • Alexander Schmitz, Josef G. Steinebach

    Pages 159-174

11. Testing for homogeneity of variance in the wavelet domain.

    • Olaf Kouamo, Eric Moulines, Francois Roueff

    Pages 175-205

12. Back Matter

    Pages 206-208

    PDF

This volume collects recent works on weakly dependent, long-memory and multifractal processes and introduces new dependence measures for studying complex stochastic systems. Other topics include the statistical theory for bootstrap and permutation statistics for infinite variance processes, the dependence structure of max-stable processes, and the statistical properties of spectral estimators of the long memory parameter. The asymptotic behavior of Fejér graph integrals and their use for proving central limit theorems for tapered estimators are investigated. New multifractal processes are introduced and their multifractal properties analyzed. Wavelet-based methods are used to study multifractal processes with different multiresolution quantities, and to detect changes in the variance of random processes. Linear regression models with long-range dependent errors are studied, as is the issue of detecting changes in their parameters.

• Estimator
• Measure
• STATISTICA
• bootstrap
• change-point detection
• linear regression
• long memory
• multifractality
• wavelets
• weak dependence

• UFR Sciences-Techniques, Pontoise, France

  Paul Doukhan

• , UMR MIA 518, INRA AgroParisTech, Paris, France

  Gabriel Lang

• Stochastic Processes Department, Vilnius, Lithuania

  Donatas Surgailis

• Aarhus University, School of Economics, CREATES, Aarhus C, Denmark

  Gilles Teyssière

Policies and ethics