Totally Positive Regression: E-Optimal Designs

by Heiligers, B.


Preprint series: 00-20, Preprints

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 \xb4\xb4almost`` 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.

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