Euclidean Design Theory. 1st ed. 2019

種類:

電子ブック

責任表示:

by Masanori Sawa, Masatake Hirao, Sanpei Kageyama

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2019

著者名:

• Sawa, Masanori.
• Hirao, Masatake.
• Kageyama, Sanpei.
• SpringerLink (Online service)

シリーズ名:

JSS Research Series in Statistics ;

ISBN:

9789811380754 [9811380759]    

注記:

Chapter I: Reproducing Kernel Hilbert Space -- Chapter II: Cubature Formula -- Chapter III: Optimal Euclidean Design -- Chapter IV: Constructions of Optimal Euclidean Design -- Chapter V: Euclidean Design Theory.
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 embe

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