The Annals of Statistics
- Ann. Statist.
- Volume 36, Number 3 (2008), 1404-1434.
Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
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(⋅).
Ann. Statist., Volume 36, Number 3 (2008), 1404-1434.
First available in Project Euclid: 26 May 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G18: Self-similar processes
Secondary: 62G30: Order statistics; empirical distribution functions
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