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(⋅).
"Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles." Ann. Statist. 36 (3) 1404 - 1434, June 2008. https://doi.org/10.1214/009053607000000587