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E-Optimal Designs for Polynomial Regression without Intercept, rev.

by Chang, F.-C., Heiligers, B..

Series: 1995-19, Preprints

62K05 Optimal designs

give all E-optimal designs for the mean parameter vector in polynomial
regression of degree d without intercept in one real variable. The deviation is
based on interlays 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 heteoscedastic
setups) are also given.