Dependence in Probability and Statistics

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Paul Doukhan
348 g
236x158x15 mm
200, Lecture Notes in Statistics

This volume provides the reader with a comprehensive recent account on dependent stochastic processes This book is a reference book for theoretical works, and provides some results that are of straight practical interest for the applied statistician/econometrician
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..
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.

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