The Annals of Statistics

Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles

Jean-François Coeurjolly

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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(⋅).

Article information

Ann. Statist., Volume 36, Number 3 (2008), 1404-1434.

First available in Project Euclid: 26 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes
Secondary: 62G30: Order statistics; empirical distribution functions

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


Coeurjolly, Jean-François. Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. Ann. Statist. 36 (2008), no. 3, 1404--1434. doi:10.1214/009053607000000587.

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