Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
Jean-François Coeurjolly
Source: Ann. Statist. Volume 36, Number 3
(2008), 1404-1434.
Abstract
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 k−αL(k) for some α>0 and some slowly varying function L(⋅).
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Keywords: Locally self-similar Gaussian process; fractional Brownian motion; Hurst exponent estimation; Bahadur representation of sample quantiles
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1211819569
Digital Object Identifier: doi:10.1214/009053607000000587
Zentralblatt MATH identifier: 1157.60034
Mathematical Reviews number (MathSciNet): MR2418662
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