Dependence in Probability and Statistics

✍ Scribed by István Berkes, Lajos Horváth, Johannes Schauer (auth.), Paul Doukhan, Gabriel Lang, Donatas Surgailis, Gilles Teyssière (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2010
• Tongue: English
• Leaves: 224
• Series: Lecture Notes in Statistics 200
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Permutation and bootstrap statistics under infinite variance....Pages 1-20
Max–Stable Processes: Representations, Ergodic Properties and Statistical Applications....Pages 21-42
Best attainable rates of convergence for the estimation of the memory parameter....Pages 43-57
Harmonic analysis tools for statistical inference in the spectral domain....Pages 59-70
On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time....Pages 71-101
Multifractal scenarios for products of geometric Ornstein-Uhlenbeck type processes....Pages 103-122
A new look at measuring dependence....Pages 123-142
Robust regression with infinite moving average errors....Pages 143-157
A note on the monitoring of changes in linear models with dependent errors....Pages 159-174
Testing for homogeneity of variance in the wavelet domain.....Pages 175-205
Back Matter....Pages 206-208

✦ Subjects

Statistics and Computing/Statistics Programs; Statistical Theory and Methods