Dependence in Probability and Statistics

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.

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.

Permutation and bootstrap statistics under infinite variance.- Max-Stable Processes: Representations, Ergodic Properties and Statistical Applications.- Best attainable rates of convergence for the estimation of the memory parameter.- Harmonic analysis tools for statistical inference in the spectral domain.- On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time.- Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes.- A new look at measuring dependence.- Robust regression with infinite moving average errors.- A note on the monitoring of changes in linear models with dependent errors.- Testing for homogeneity of variance in the wavelet domain..