95-19
E-Optimal Designs for Polynomial Regression without Intercept, rev.
by Chang, F.-C.; Heiligers, B.
Preprint series: 95-19, Preprints
- MSC:
- 62K05 Optimal designs
Abstract: We give all E-optimal designs for the mean parameter vector in polynomialregression of degree d without intercept in one real variable. The deviation isbased on interlays between E-optimal design problems in the present and incertain heteroscedastic polynomial setups with intercept. Thereby the optimalsupports are found to be related to the alternation points of the Chebyshevpolynomials of the first kind, but the structure of optimal designs essentiallydepends on the regression degree being odd or even. In the former case theE-optimal designs are precisely the (infinitely many) scalar optimal designs,where the scalar parameter system refers to the Chebyshev coefficients, whilefor even d there is exactly one optimal design. In both cases explicit formulaefor the corresponding optimal weights are obtained. Remarks on extending theresults to E-optimality for subparameters of the mean vector (in heteoscedasticsetups) are also given.