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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130795This 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 non-linear functions of Gaussians sequences with correlation function decreasing as $k^{-α}L(k)$ for some $α>0$ and some slowly varying function $L(\cdot)$.44 pages, février 2007Statistics Theory60G18, 62G30Hurst exponent estimation of locally self-similar Gaussian processes using sample quantilestext