  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
$\rho(i)\sim \kappa|i|^{-\alpha}$ ($\kappa\in \RR$) with $\alpha>0$. 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.
