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June 2008 Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
Jean-François Coeurjolly
Ann. Statist. 36(3): 1404-1434 (June 2008). DOI: 10.1214/009053607000000587


This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0, 1]. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of nonlinear functions of Gaussian sequences with correlation function decreasing as kαL(k) for some α>0 and some slowly varying function L(⋅).


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Jean-François Coeurjolly. "Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles." Ann. Statist. 36 (3) 1404 - 1434, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1157.60034
MathSciNet: MR2418662
Digital Object Identifier: 10.1214/009053607000000587

Primary: 60G18
Secondary: 62G30

Keywords: Bahadur representation of sample quantiles , fractional Brownian motion , Hurst exponent estimation , Locally self-similar Gaussian process

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 3 • June 2008
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