Totally positive regression: E-optimal designs

被引：0
作者：
Heiligers B. [1 ]
机构：
[1] Fakultät für Mathematik, Inst. für Math. Stochastik, Universität Magdeburg
来源：
Metrika | 2002年 / 54卷 / 3期
关键词：
Approximate design; Chebyshev approximation; Chebyshev system; E-optimality; Equi-oscillation; Polynomial splines; Scalar optimality; Total positivity; Weighted polynomial regression;
D O I：
10.1007/s184-002-8364-7
中图分类号：
学科分类号：
摘要：
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.
引用
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页码：191 / 213
页数：22
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