T-optimal designs for discrimination between two polynomial models

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dc.contributor.authorDette, Holger
dc.contributor.authorMelas, Viatcheslav B.
dc.contributor.authorShpilev, Petr
dc.date.accessioned2011-07-21T10:07:03Z
dc.date.available2011-07-21T10:07:03Z
dc.date.issued2011-07-21
dc.description.abstractThe paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree n−2 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^(n−1) 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 n∈N. 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^(n−1) 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.en
dc.identifier.urihttp://hdl.handle.net/2003/28941
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-1899
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;23/2011
dc.subjectChebyshev polynomialsen
dc.subjectdiscrimination designsen
dc.subjectgoodness-of-fit testen
dc.subjectmodel uncertaintyen
dc.subjectT-optimum designen
dc.subjectuniform approximationen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleT-optimal designs for discrimination between two polynomial modelsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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