从属高斯过程的期望及其应用
Expectiles for subordinated Gaussian processes with applications
摘要：
本文引入了分数布朗运动（fBm）过程Hurst指数的一类新的估计。这些估计是基于fBM过程的样本路径的离散变化的样本期望。为了得到估计的统计性质，我们建立了单位方差和相关函数满足$ρ(i)\sim κ|i|^{-α}$（$κ\in \RR$）和$α>0$的从属平稳高斯过程的样本期望的渐近结果.通过模拟研究，我们证明了相关的期望为基础的估计方法，并表明，建议的估计是更强大的数据舍入比他们的样本分位数为基础的同行。
英文摘要：
In this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample expectiles of subordinated stationary Gaussian processes with unit variance and correlation function satisfying $ρ(i)\sim κ|i|^{-α}$ ($κ\in \RR$) with $α>0$. Via a simulation study, we demonstrate the relevance of the expectile-based estimation method and show that the suggested estimators are more robust to data rounding than their sample quantile-based counterparts.
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