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Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems | | J.-R. Chazottes
; P. Collet
; B. Schmitt
; | | Date: |
8 Dec 2004 | | Subject: | Dynamical Systems; Probability | math.DS math.PR | | Abstract: | In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space. | | Source: | arXiv, math.DS/0412167 | | Services: | Forum | Review | PDF | Favorites | |
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