Heiligers, Berthold Totally positive regression: E-optimal designs. (English) Zbl 1020.62064 Metrika 54, No. 3, 191-213 (2002). 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. Cited in 2 Documents MSC: 62K05 Optimal statistical designs 62J05 Linear regression; mixed models Keywords:approximate design; scalar optimality; Chebyshev approximation; Chebyshev system; E-optimality; equi-oscillation; polynomial splines; total positivity; weighted polynomial regression PDFBibTeX XMLCite \textit{B. Heiligers}, Metrika 54, No. 3, 191--213 (2002; Zbl 1020.62064) Full Text: DOI