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Totally Positive Regression: E-Optimal Designs

by Heiligers, B..

Series: 2000-20, Preprints

62K05 Optimal designs

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.

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