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Euclidean Design Theory

Part of the SpringerBriefs in Statistics Book Series

DOI: 10.1007/978-981-13-8075-4

ISBN: 978-981-13-8074-7

Publisher: Springer Singapore - Springer Journals

Jul 23, 2019

Available

Kernel Functions

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: 1 –17

[The present chapter provides a brief summary of basic ideas and facts concerning kernel functions, which are closely related to the theories of cubature formula being a certain class of integration formulas in numerical analysis, as well as of Euclidean design which is a special point...
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Cubature Formula

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: 19 –44

[A cubature formulaCubature formula reveals a numerical integration rule that approximates a multiple integral by a positive linear combination of function values at finitely many specified points on the integral domain. A central objective is to investigate the existence as well as the...
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Optimal Euclidean Design

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: 45 –61

[The main problem in optimal design theory is to find a finite set of observation points (design), where unknown parameters of a regression model are “well-estimated” with some statistical criterion. D-optimalityOptimality criterionD-optimality is a popular criterion that seeks for designs...
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Constructions of Optimal Euclidean Design

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: 63 –101

[The most straightforward way of replacing an optimal invariant design \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Euclidean Design Theory

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: 103 –129

[The design of experiments, which has rapidly grown in connection with a wide range of fields such as engineering, psychology, etc., and which in particular has led to the development of the statistical quality control, is one of the most important areas in applied statistics. On the other hand,...
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Correction to: Euclidean Design Theory

Sawa, Masanori; Hirao, Masatake; Kageyama, Sanpei

Pages: C1 –C2

[In the original version of the book, the following belated corrections have been made]

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