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Media type:
E-Article
Title:
Minimax Designs for Fourier Series and Spherical Harmonics Regressions: A Characterization of Rotatable Arrangements
Contributor:
Kupper, Lawrence L.
imprint:
Royal Statistical Society, 1973
Published in:Journal of the Royal Statistical Society. Series B (Methodological)
Language:
English
ISSN:
0035-9246
Origination:
Footnote:
Description:
<p>In the framework of the approximate theory of the optimal design of experiments, Hoel (1965) represented minimax designs for Fourier series and spherical harmonics regressions of order r in terms of certain normalizing coefficients which are difficult to interpret. In this paper it is shown that these designs are intimately related to rotatable arrangements of points of order r in two and three dimensions, respectively. This result is used to construct exact minimax designs for Fourier series regression of all orders and for spherical harmonics regression of orders one and two. Sequential designs and infinite classes of designs depending on only one parameter are given.</p>