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Title: Optimal designs for regression with spherical data
Authors: Dette, Holger 
Konstantinou, Maria 
Schorning, Kirsten 
Gösmann, Josua 
Major Field of Science: Natural Sciences
Field Category: Mathematics
Keywords: Hyperspherical harmonics;Optimal design;Series estimation;Φp-optimality
Issue Date: 2019
Source: Electronic Journal of Statistics, 2019, Vol. 13, No. 1, pp. 361-390
Volume: 13
Issue: 1
Start page: 361
End page: 390
Journal: Electronic Journal of Statistics 
Abstract: In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the misorientation distribution or the grain boundary distribution (depending on a four dimensional spherical predictor) are represented by series of hyperspherical harmonics, which are estimated from experimental or simulated data. For this type of estimation problems we explicitly determine optimal designs with respect to the Φ p -criteria introduced by Kiefer (1974) and a class of orthogonally invariant information criteria recently introduced in the literature. In particular, we show that the uniform distribution on the m-dimensional sphere is optimal and construct discrete and implementable designs with the same information matrices as the continuous optimal designs. Finally, we illustrate the advantages of the new designs for series estimation by hyperspherical harmonics, which are symmetric with respect to the first and second crystallographic point group.
ISSN: 1935-7524
DOI: 10.1214/18-EJS1524
Rights: © Institute of Mathematical Statistics. All rights reserved.
Type: Article
Affiliation : Ruhr-Universität Bochum 
Cyprus University of Technology 
Appears in Collections:Άρθρα/Articles

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