  Hurst exponent is an important feature summarizing the noisy high-frequency
data when the inherent scaling pattern cannot be described by standard
statistical models. In this paper, we study the robust estimation of Hurst
exponent based on non-decimated wavelet transforms (NDWT). The robustness is
achieved by applying a general trimean estimator on non-decimated wavelet
coefficients of the transformed data. The general trimean estimator is derived
as a weighted average of the distribution's median and quantiles, combining the
median's emphasis on central values with the quantiles' attention to the
extremes. The properties of the proposed Hurst exponent estimators are studied
both theoretically and numerically. Compared with other standard wavelet-based
methods (Veitch $\&$ Abry (VA) method, Soltani, Simard, $\&$ Boichu (SSB)
method, median based estimators MEDL and MEDLA), our methods reduce the
variance of the estimators and increase the prediction precision in most cases.
The proposed methods are applied to a data set in high frequency pupillary
response behavior (PRB) with the goal to classify individuals according to a
degree of their visual impairment.
