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

• 成果类型: Article
• 署名作者: Coeurjolly, Jean-Francois
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000587
• 发表日期: 2008
• 页码: 1404-1434
• 关键词: bahadur representation

摘要

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(-alpha) L(k) for some alpha > 0 and some slowly varying function L(.).