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

Estimation of the Hurst Exponent Using Trimean Estimators on Nondecimated Wavelet Coefficients