Title: An empirical evaluation of alternative methods of estimation for Permutation Entropy in time series with tied values,
Abstract: Bandt and Pompe introduced Permutation Entropy in 2002 for Time Series where
equal values, xt1 = xt2, t1 = t2, were neglected and only inequalities between
the xt were considered. Since then, this measure has been modified and
extended, in particular in cases when the amount of equal values in the series
can not be neglected, (i.e. heart rate variability (HRV) time series). We
review the different existing methodologies that treats this subject by
classifying them according to their different strategies. In addition, a novel
Bayesian Missing Data Imputation is presented that proves to outperform the
existing methodologies that deals with type of time series. All this facts are
illustrated by simulations and also by distinguishing patients suffering from
Congestive Heart Failure from a (healthy) control group using HRV time series