Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/77243
Authors: 
Dette, Holger
Franke, Tobias
Year of Publication: 
2000
Series/Report no.: 
Technical Report, SFB 475: Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2000,38
Abstract: 
In the common polynomial regression of degree m we determine the design which maximizes the minimum of the D-efficiency in the model of degree m and the D-efficiencies in the models of degree m – j,…, m + k (j, k > 0 given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree m by testing the highest coefficients in the polynomials of degree m – j, … ; m + k. Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.
Subjects: 
Minimax optimal designs
robust design
D-optimality
D1-optimality
t-test
associated orthogonal polynomials
Document Type: 
Working Paper

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