Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
复制标题
DOI：
10.1214/009053607000000587
复制
发表时间：
2008-06-01
影响因子：
4.5
通讯作者：
Coeurjolly, Jean-Francois
中科院分区：
文献类型：
--
作者：
Coeurjolly, Jean-Francois
本文给出了局部自相似高斯过程分形维数的一类新的相合估计。这些估计量基于区间[0，1]的离散网格上样本路径离散变化的样本分位数的凸组合。我们得到了这些估计的几乎处处收敛性和渐近正态性。关键成分是高斯序列的非线性函数的样本分位数的Bahadur表示，其中相关函数随着k（-alpha）L（k）而减小，对于某些alpha > 0和某些缓慢变化的函数L（.）。
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(.).