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(⋅).
@article{1211819569,
author = {Coeurjolly, Jean-Fran\c cois},
title = {Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1404-1434},
language = {en},
url = {http://dml.mathdoc.fr/item/1211819569}
}
Coeurjolly, Jean-François. Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. Ann. Statist., Tome 36 (2008) no. 1, pp. 1404-1434. http://gdmltest.u-ga.fr/item/1211819569/