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

Jean-François Coeurjolly (1)

1 SAGAG - Statistique Appliquée et de Géométrie Aléatoire de Grenoble

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 non-linear functions of Gaussians sequences with correlation function decreasing as $k^{-\alpha}L(k)$ for some $\alpha>0$ and some slowly varying function $L(\cdot)$.

Mots clés: locally self-similar Gaussian process; fractional Brownian motion; Hurst exponent estimation; Bahadur representation of sample quantiles

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-François Coeurjolly. Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. Annals of Statistics, 2008, 36 (3), pp.1404-1434. ⟨10.1214/009053607000000587⟩. ⟨hal-00005371v2⟩