by Heiligers, B..

**Series:** 2000-20, Preprints

- MSC:
- 62K05 Optimal designs

**Abstract:**

E-optimality of approximate designs in linear regression

models is paired with a dual problem of nonlinear Chebyshev

approximation. When the regression functions form a totally

positive system, then the information matrices of designs

for subparameters turn out to be ´´almost`` totally positive,

a property which, together with the duality, allows to

solve the nonlinear Chebyshev problem. Thereby we obtain

explicit formular for E-optimal designs in terms of

equi-oscillating generalized polynomials. The considerations

unify and generalize known results on E-optimality, found

in particular regression setups.

**Keywords:**

Approximate design, scalar optimality, Chebyshev approximation, Chebyshev system, E-optimality, equi-oscillation, polynomial splines, total positivity, weighted polynomial regression.