Related references
Note: Only part of the references are listed.
Article
Physics, Multidisciplinary
Andrea A. Rey et al.
Summary: The study provides expressions for asymptotic distributions of Renyi and Tsallis of order q entropies and Fisher information, computed on the maximum likelihood estimator of probabilities from multinomial random samples. It is verified that these asymptotic models, including the normal Tsallis and Fisher, effectively describe various simulated data. Additionally, the study presents test statistics for comparing entropies from two samples, potentially with different categories. The tests are applied to social survey data, showing consistent and more general results compared to a χ² test.
Article
Physics, Mathematical
José M. Amigó et al.
Article
Statistics & Probability
Eduarda T. C. Chagas et al.
Summary: This article presents the Bandt and Pompe methodology for time series analysis and its statistical properties. It proposes a test in the entropy-complexity plane for the white noise hypothesis, which is validated using true white noise sequences. The results show that the proposed methodology provides consistent and reliable results.
INTERNATIONAL STATISTICAL REVIEW
(2022)
Article
Physics, Multidisciplinary
Inmaculada Leyva et al.
Summary: Ordinal Analysis is a new methodology for analyzing complex time series, which calculates the ordinal patterns and probabilities to obtain the permutation entropy. It has been widely applied in various fields, but there are still unresolved challenges in combining ordinal analysis with machine learning techniques.
Article
Mathematics, Applied
Arthur Matsuo Yamashita Rios de Sousa et al.
Summary: We extended Elsinger's work on chi-squared tests for independence using ordinal patterns and investigated a general class of m-dependent ordinal patterns processes. We proposed a test method to quantify the range of serial dependence in a process, and applied it to epilepsy electroencephalography time series data.
Article
Mathematics, Applied
E. T. C. Chagas et al.
Summary: The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, this study aims to understand the joint distribution of pair entropy-statistical complexity for a large class of time series models, which can enable new statistical tests. By applying the central limit theorem, multivariate delta method, and a third-order correction, the study characterizes the asymptotic distribution of empirical Shannon's entropy for any model with a true normalized entropy between zero and one. The study also proposes a bilateral test to examine if two signals produce ordinal patterns with the same Shannon's entropy and applies it to daily maximum temperature time series from three cities, obtaining sensible results.
Article
Engineering, Electrical & Electronic
Eduarda T. C. Chagas et al.
Summary: The paper introduces a new technique for texture analysis and classification of SAR data based on Bandt-Pompe symbolization. It linearizes 2-D patches of the image and builds ordinal pattern transition graph to characterize textures, showing effectiveness in homogeneous areas with satisfactory separability levels. The technique uses simple and quick-to-calculate descriptors as features for a k-nearest neighbor classifier, presenting results similar to state-of-the-art techniques with higher computational costs.
IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING
(2021)
Article
Physics, Multidisciplinary
C Bandt et al.
PHYSICAL REVIEW LETTERS
(2002)
Article
Engineering, Biomedical
GA Moody et al.
IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE
(2001)
