Totally positive regression: E-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 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.
scientific article; zbMATH DE number 1887584