Overview
- Covers the constructions of optimal experimental designs comprehensively
- Provides a novel framework for understanding optimal designs, based on the theory of cubature formulas in analysis and spherical/Euclidean designs in combinatorics
- Presents a fresh approach for introducing the theory of the cubature formula with reproducing kernel Hilbert space in functional analysis
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (6 chapters)
Keywords
About this book
This book is the modern first treatment of experimental designs, providing a comprehensive introduction to the interrelationship between the theory of optimal designs and the theory of cubature formulas in numerical analysis. It also offers original new ideas for constructing optimal designs.
The book opens with some basics on reproducing kernels, and builds up to more advanced topics, including bounds for the number of cubature formula points, equivalence theorems for statistical optimalities, and the Sobolev Theorem for the cubature formula. It concludes with a functional analytic generalization of the above classical results.
Although it is intended for readers who are interested in recent advances in the construction theory of optimal experimental designs, the book is also useful for researchers seeking rich interactions between optimal experimental designs and various mathematical subjects such as spherical designs in combinatorics and cubature formulas in numerical analysis, both closely related to embeddings of classical finite-dimensional Banach spaces in functional analysis and Hilbert identities in elementary number theory. Moreover, it provides a novel communication platform for “design theorists” in a wide variety of research fields.
Reviews
“This book can be used in a PhD course for mathematicians or statisticians with a solid background in numerical analysis, and can be used as a reference for researchers who need to use Euclidean designs or cubature formulae or both.” (Fabio Rapallo, Mathematical Reviews, October, 2020)
Authors and Affiliations
About the authors
Masanori Sawa received his M.S. degree in Mathematics from Hiroshima University in 2005 and Ph.D. degree in Information Science from Nagoya University in 2007. He was a postdoctoral fellow with the Japan Society for the Promotion of Science, a lecturer at the Takamatsu National College of Technology, and an Assistant Professor at Nagoya University. He has been an Associate Professor at the Graduate School of System Informatics, Kobe University, Japan, since 2014. His current research interests include algebraic combinatorics, numerical analysis and mathematical statistics.
Masatake Hirao received his M.S. and Ph.D. degrees in Information Science from Nagoya University, Japan, in 2006 and 2010, respectively. He has been an Associate Professor at the School of Information and Science Technology, Aichi Prefectural University, Japan, since 2014. His research interests are mathematical statistics, probability theory, combinatorics and numerical analysis.Sanpei Kageyama has been a Visiting Professor of Statistics and Discrete Mathematics at the Research Center for Mathmatics and Science Education, Tokyo University of Science, Japan, since 2016. He is now an Emeritus Professor of Hiroshima University. He has published over 340 articles in scientific journals. He was a Foundation Fellow of the Institute of Combinatorics and its Applications, and a council member of the Mathematical Society of Japan, the Japan Statistical Society, and Japanese Society of Applied Statistics. He has also served on the editorial boards of Utilitas Mathematics, Journal of Statistical Planning and Inference, Discussiones Mathematicae, Sankhya, and the Journal of Statistics and Applications.
Bibliographic Information
Book Title: Euclidean Design Theory
Authors: Masanori Sawa, Masatake Hirao, Sanpei Kageyama
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-13-8075-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019
Softcover ISBN: 978-981-13-8074-7Published: 07 October 2019
eBook ISBN: 978-981-13-8075-4Published: 23 July 2019
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: VIII, 134
Number of Illustrations: 2 b/w illustrations, 12 illustrations in colour
Topics: Statistical Theory and Methods, Statistics and Computing/Statistics Programs, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Statistics for Business, Management, Economics, Finance, Insurance