The Annals of Statistics

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

Jean-François Coeurjolly

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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 kαL(k) for some α>0 and some slowly varying function L(⋅).

Article information

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

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1211819569

Digital Object Identifier
doi:10.1214/009053607000000587

Mathematical Reviews number (MathSciNet)
MR2418662

Zentralblatt MATH identifier
1157.60034

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1211819569


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