# Confidence Intervals and Hypothesis Testing for the Permutation Entropy with an application to Epilepsy

## TL;DR

This paper introduces a bootstrap-based statistical method to accurately estimate the variability of Permutation Entropy in time series, with applications to detecting epileptic activity in EEG signals.

## Contribution

It proposes a novel parametric bootstrap approach for assessing the accuracy of Permutation Entropy, addressing a gap in statistical analysis of this complexity measure.

## Key findings

- The method performs well on stochastic process simulations.
- It provides reliable confidence intervals for Permutation Entropy estimates.
- Application to EEG data distinguishes normal from pre-ictal states.

## 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.