T-optimal designs for discrimination between two polynomial models / Holger Dette, Viatcheslav B. Melas, Petr Shpilev
VerfasserDette, Holger ; Melas, Vjačeslav Borisovič ; Shpilev, Petr
Erschienen[Dortmund] : SFB 823, 2011
Elektronische Ressource
Umfang1 Online-Ressource (14 Seiten) : Diagramme
SerieDiscussion paper ; Nr. 23 (2011)
SchlagwörterPolynom / Regressionsmodell
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T-optimal designs for discrimination between two polynomial models [0.26 mb]

The paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree n2 and n. In a fundamental paper Atkinson and Fedorov (1975a) proposed the T-optimality criterion for this purpose. Recently Atkinson (2010) determined T-optimal designs for polynomials up to degree 6 numerically and based on these results he conjectured that the support points of the optimal design are cosines of the angles that divide a half of the circle into equal parts if the coefficient of x^(n1) in the polynomial of larger degree vanishes. In the present paper we give a strong justification of the conjecture and determine all T-optimal designs explicitly for any degree nN. In particular, we show that there exists a one-dimensional class of T-optimal designs. Moreover, we also present a generalization to the case when the ratio between the coefficients of x^(n1) and x^n is smaller than a certain critical value. Because of the complexity of the optimization problem T-optimal designs have only been determined numerically so far and this paper provides the first explicit solution of the T-optimal design problem since its introduction by Atkinson and Fedorov (1975a). Finally, for the remaining cases (where the ratio of coefficients is larger than the critical value) we propose a numerical procedure to calculate the T-optimal designs. The results are also illustrated in an example.

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