Title: Confidence Intervals and Hypothesis Testing for the Permutation Entropy with an application to Epilepsy,
Abstract: In nonlinear dynamics, and to a lesser extent in other fields, a widely used
measure of complexity is the Permutation Entropy. But there is still no known
method to determine the accuracy of this measure. There has been little
research on the statistical properties of this quantity that characterize time
series. The literature describes some resampling methods of quantities used in
nonlinear dynamics - as the largest Lyapunov exponent - but all of these seems
to fail. In this contribution we propose a parametric bootstrap methodology
using a symbolic representation of the time series in order to obtain the
distribution of the Permutation Entropy estimator. We perform several time
series simulations given by well known stochastic processes: the 1=f? noise
family, and show in each case that the proposed accuracy measure is as
efficient as the one obtained by the frequentist approach of repeating the
experiment. The complexity of brain electrical activity, measured by the
Permutation Entropy, has been extensively used in epilepsy research for
detection in dynamical changes in electroencephalogram (EEG) signal with no
consideration of the variability of this complexity measure. An application of
the parametric bootstrap methodology is used to compare normal and pre-ictal
EEG signals.