Dependence in Probability and Statistics

1. Auflage 2010
ISBN: 978-3-642-14103-4
Verlag: Springer

Buch, Englisch, 205 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 720 g

Reihe: Lecture Notes in Statistics

This volume contains several contributions on the general theme of dependence for several classes of stochastic processes, andits implicationson asymptoticproperties of various statistics and on statistical inference issues in statistics and econometrics. The chapter by Berkes, Horváth and Schauer is a survey on their recent results on bootstrap and permutation statistics when the negligibility condition of classical central limit theory is not satis ed. These results are of interest for describing the asymptotic properties of bootstrap and permutation statistics in case of in nite va- ances, and for applications to statistical inference, e.g., the change-point problem. The paper by Stoev reviews some recent results by the author on ergodicity of max-stable processes. Max-stable processes play a central role in the modeling of extreme value phenomena and appear as limits of component-wise maxima. At the presenttime,arathercompleteandinterestingpictureofthedependencestructureof max-stable processes has emerged,involvingspectral functions, extremalstochastic integrals, mixed moving maxima, and other analytic and probabilistic tools. For statistical applications, the problem of ergodicity or non-ergodicity is of primary importance.

Zielgruppe

Research

Autoren/Hrsg.

Doukhan, Paul

Lang, Gabriel

Surgailis, Donatas

Teyssière, Gilles

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

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.