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010   $a981-13-8075-9
024 7 $a10.1007/978-981-13-8075-4
035   $a(CKB)4100000008876861
035   $a(MiAaPQ)EBC5836940
035   $a(DE-He213)978-981-13-8075-4
035   $a(PPN)238486389
035   $a(MiAaPQ)EBC6225088
035   $a(EXLCZ)994100000008876861
100   $a20190723d2019      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aEuclidean Design Theory /$fby Masanori Sawa, Masatake Hirao, Sanpei Kageyama
205   $a1st ed. 2019.
210  1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2019.
215   $a1 online resource (139 pages)
225 1 $aJSS Research Series in Statistics,$x2364-0065
311 08$a981-13-8074-0 
327   $aChapter 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.
330   $aThis book is the modern first treatment of experimental designs, providing a comprehensive introduction to the interrelationship between the theory of optimal designs and the theory of cubature formulas in numerical analysis. It also offers original new ideas for constructing optimal designs. The book opens with some basics on reproducing kernels, and builds up to more advanced topics, including bounds for the number of cubature formula points, equivalence theorems for statistical optimalities, and the Sobolev Theorem for the cubature formula. It concludes with a functional analytic generalization of the above classical results. Although it is intended for readers who are interested in recent advances in the construction theory of optimal experimental designs, the book is also useful for researchers seeking rich interactions between optimal experimental designs and various mathematical subjects such as spherical designs in combinatorics and cubature formulas in numerical analysis, both closely related to embeddings of classical finite-dimensional Banach spaces in functional analysis and Hilbert identities in elementary number theory. Moreover, it provides a novel communication platform for ?design theorists? in a wide variety of research fields.
410  0$aJSS Research Series in Statistics,$x2364-0065
606   $aStatistics
606   $aMathematical statistics$xData processing
606   $aStatistics
606   $aStatistical Theory and Methods
606   $aStatistics and Computing
606   $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences
606   $aStatistics in Business, Management, Economics, Finance, Insurance
615  0$aStatistics.
615  0$aMathematical statistics$xData processing.
615  0$aStatistics.
615 14$aStatistical Theory and Methods.
615 24$aStatistics and Computing.
615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
615 24$aStatistics in Business, Management, Economics, Finance, Insurance.
676   $a519.5
700   $aSawa$b Masanori$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781851
702   $aHirao$b Masatake$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aKageyama$b Sanpei$f1945-$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910350245803321
996   $aEuclidean Design Theory$92523258
997   $aUNINA