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

**Series:** 1995-19, Preprints

- MSC:
- 62K05 Optimal designs

**Abstract:**

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.

**Keywords:**