Authors:
- Helps readers understand entropy and its properties for data analysis
- Reconsiders statistical methods from the point of view of entropy and provides new insights for data analysis
- Explains the applicability of entropy for creating new statistical methods
Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior (BQAHB, volume 3)
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Table of contents (8 chapters)
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Front Matter
About this book
This book reconsiders statistical methods from the point of view of entropy, and introduces entropy-based approaches for data analysis. Further, it interprets basic statistical methods, such as the chi-square statistic, t-statistic, F-statistic and the maximum likelihood estimation in the context of entropy. In terms of categorical data analysis, the book discusses the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) for measuring association and/or predictive powers in association models, and generalized linear models (GLMs). Through association and GLM frameworks, it also describes ECC and ECD in correlation and regression analyses for continuous random variables. In multivariate statistical analysis, canonical correlation analysis, T2-statistic, and discriminant analysis are discussed in terms of entropy. Moreover, the book explores the efficiency of test procedures in statistical tests of hypothesesusing entropy. Lastly, it presents an entropy-based path analysis for structural GLMs, which is applied in factor analysis and latent structure models. Entropy is an important concept for dealing with the uncertainty of systems of random variables and can be applied in statistical methodologies. This book motivates readers, especially young researchers, to address the challenge of new approaches to statistical data analysis and behavior-metric studies.
Authors and Affiliations
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Center for Educational Outreach and Admissions, Kyoto University, Kyoto, Japan
Nobuoki Eshima
About the author
Nobuoki Eshima was born in Fukuoka, Japan in 1957. He was received B. Sc. and D. Sc. degrees in Mathematics from Kyushu University, Fukuoka, Japan in 1980 and 1993, respectively. In 1993, he joined Department of Statistics, Faculty of General Education, Nagasaki University as Associate Professor. In 1996, he joined Department of Medical Information Analysis, Faculty of Medicine, Oita Medical University as Professor. Since 2003 he is working as a Professor in Faculty of Medicine, Oita University, where the name of affiliation has changed because of combining with another university. From 2016, he is a professor of Center for Educational Outreach and Admissions, Kyoto University. He is an elected member of International Statistical Institute (ISI) and a reviewer for Mathematical Reviews of the American Mathematical Society (AMS).
Bibliographic Information
Book Title: Statistical Data Analysis and Entropy
Authors: Nobuoki Eshima
Series Title: Behaviormetrics: Quantitative Approaches to Human Behavior
DOI: https://doi.org/10.1007/978-981-15-2552-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2020
Hardcover ISBN: 978-981-15-2551-3Published: 22 January 2020
Softcover ISBN: 978-981-15-2554-4Published: 22 January 2021
eBook ISBN: 978-981-15-2552-0Published: 21 January 2020
Series ISSN: 2524-4027
Series E-ISSN: 2524-4035
Edition Number: 1
Number of Pages: XI, 257
Number of Illustrations: 43 b/w illustrations
Topics: Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Statistical Theory and Methods, Statistics for Social Sciences, Humanities, Law, Statistics for Business, Management, Economics, Finance, Insurance