Characterizing D-optimal Rotatable Designs with Finite Reflection Groups

Masanori Sawa () and Masatake Hirao ()
Additional contact information
Masanori Sawa: Kobe University
Masatake Hirao: Aichi Prefectural University

Sankhya A: The Indian Journal of Statistics, 2017, vol. 79, issue 1, No 5, 132 pages

Abstract: Abstract We establish a powerful construction of D-optimal Euclidean designs, or D-optimal rotatable designs, on the unit hyperball by using the corner vectors associated with the symmetry groups of (semi-)regular polytopes. This is a full generalization of the classical construction choosing points in the form (a,…,a,0,…,0) or in their orbits under the symmetry group of a regular hyperoctahedron (Gaffke and Heiligers 1995b), (Hirao et al. 2014), as well as Scheffé’s {n, 2}-lattice design on the simplex. We prove a Gaffke-Heiligers type theorem for D n - and A n -invariant D-optimal Euclidean designs which is a “reduction theorem” on the computational cost of searching observation points, and thereby construct many families of D-optimal Euclidean designs. For each group A n , D n , B n , H 3, H 4, F 4, E 6, E 7, E 8, we determine the maximum degree of a D-optimal Euclidean design constructed by our method and in particular discover examples of degrees 5 and 6 for E 8 and H 4, respectively. We also classify such maximum-degree designs for the groups H 3, H 4 and F 4 acting on the 3- and 4-dimensional Euclidean spaces.

Keywords: Approximate design; Optimal design; Euclidean design; Corner-vector method; D-optimality; Finite irreducible reflection group; Gaffke-Heiligers theorem; Invariant harmonic polynomial; 62K05; 65D32; 05E99 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-016-0091-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:79:y:2017:i:1:d:10.1007_s13171-016-0091-1

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-016-0091-1

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().