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 allows to solve the nonlinear Chebyshev problem. Thereby we obtain explicit formulae for E-optimal designs in terms of equi-oscillating generalized polynomials. The considerations unify and generalize known results on E-optimality for particular regression setups.
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Heiligers, B. Totally positive regression: E-optimal designs. Metrika 54, 191–213 (2002). https://doi.org/10.1007/s184-002-8364-7
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DOI: https://doi.org/10.1007/s184-002-8364-7