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E-optimal designs for polynomial regression without intercept

✍ Scribed by Fu-Chuen Chang; Berthold Heiligers

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
863 KB
Volume
55
Category
Article
ISSN
0378-3758

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✦ Synopsis

We give all E-optimal designs for the mean parameter vector in polynomial regression of degree d without intercept in one real variable. The derivation is based on interplays between E-optimal design problems in the present and in certain heteroscedastic polynomial setups with intercept. Thereby the optimal supports are found to be related to the alternation points of the Chebyshev polynomials of the first kind, but the structure of optimal designs essentially depends on the regression degree being odd or even. In the former case the E-optimal designs are precisely the (infinitely many) scalar optimal designs, where the scalar parameter system refers to the Chebyshev coefficients, while for even d there is exactly one optimal design. In both cases explicit formulae for the corresponding optimal weights are obtained. Remarks on extending the results to E-optimality for subparameters of the mean vector (in heteroscdastic setups) are also given.

πŸ“œ SIMILAR VOLUMES

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By utilizing the equivalence theorem and Descartes's rule of signs, we construct D-optimal designs for a weighted polynomial regression model of degree k, with speciΓΏc weight function w(x) = 1=(a 2 -x 2 ) , on the compact interval [ -1; 1]. The main result shows that in most cases, the number of sup