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A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle

A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle
A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle
We investigate the D-optimal design problem in the common trigonometric regression model, where the design space is a partial circle. The task of maximizing the criterion function is transformed into the problem of determining an eigenvalue of a certain matrix via a differential equation approach. Since this eigenvalue is an analytic function of the length of the design space, we can make use of a Taylor expansion to provide a recursive algorithm for its calculation. Finally, this enables us to determine Taylor expansions for the support points of the D-optimal design.
trigonometric regression, d-optimality, implicit function theorem, differential equation
0167-7152
389-397
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Melas, V.B.
ade19d15-ba99-4afe-a5c2-555412f27d52
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Melas, V.B.
ade19d15-ba99-4afe-a5c2-555412f27d52
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039

Dette, Holger, Melas, V.B. and Biedermann, Stefanie (2002) A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle. Statistics and Probability Letters, 58 (4), 389-397. (doi:10.1016/S0167-7152(02)00152-9).

Record type: Article

Abstract

We investigate the D-optimal design problem in the common trigonometric regression model, where the design space is a partial circle. The task of maximizing the criterion function is transformed into the problem of determining an eigenvalue of a certain matrix via a differential equation approach. Since this eigenvalue is an analytic function of the length of the design space, we can make use of a Taylor expansion to provide a recursive algorithm for its calculation. Finally, this enables us to determine Taylor expansions for the support points of the D-optimal design.

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More information

Published date: 2002
Additional Information: Short communication
Keywords: trigonometric regression, d-optimality, implicit function theorem, differential equation
Organisations: Statistics

Identifiers

Local EPrints ID: 41841
URI: http://eprints.soton.ac.uk/id/eprint/41841
ISSN: 0167-7152
PURE UUID: 7f9297e8-6009-47f0-820a-b8d86a247734
ORCID for Stefanie Biedermann: ORCID iD orcid.org/0000-0001-8900-8268

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Date deposited: 10 Oct 2006
Last modified: 18 Feb 2021 17:07

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