Alzheimer disease diagnostics from EEG via Wishart distribution of fractional processes

Abstract

Exact estimation of Hurst exponent from a signal is a complex task that determines the fractional character of the investigated sample. In this work, we propose a maximum likelihood technique using Wishart distribution and autocorrelation structure of the investigated time series. Unlike conventional methods, we perform signal segmentation and use the aggregated data to obtain an unbiased estimate of Hurst exponent. The efficiency of the estimation is validated by four different methods of fractional Brownian motion generation. The resulting estimates have very tiny confidence intervals as well as small mean square error. Additionally, the proposed methodology has been applied to 19-channel EEG time series and their Hurst exponent estimation related to the diagnostics of Alzheimer’s disease.