Approximate entropy: Statistical properties and applications

ApEn, approximate entropy, is a recently developed family of parameters and statistics quantifying regularity (complexity) in data, providing an information-theoretic quantity for continuous-state processes. We provide the motivation for ApEn development, and indicate the superiority of ApEn to the K-S entropy for statistical application, and for discrimination of both correlated stochastic and noisy deterministic processes. We study the variation of ApEn with input parameter choices, reemphasizing that ApEn is a relative measure of regularity. We study the bias in the ApEn statistic, and present evidence for asymptotic normality in the ApEn distributions, assuming weak dependence. We provide a new test for the hypothesis that an underlying time-series is generated by i.i.d. variables, which does not require distribution specification. We introduce randomized ApEn, which derives an empirical significance probability that two processes differ, based on one data set from each process.