On representing maximin efficient designs by Taylor series

Melas, V. and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2007. On representing maximin efficient designs by Taylor series. Journal of Statistical Planning and Inference 137 (8) , pp. 2689-2702. 10.1016/j.jspi.2005.05.006

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Abstract

This paper considers exponential and rational regression models that are nonlinear in some parameters. Recently, locally D-optimal designs for such models were investigated in [Melas, V. B., 2005. On the functional approach to optimal designs for nonlinear models. J. Statist. Plann. Inference 132, 93–116] based upon a functional approach. In this article a similar method is applied to construct maximin efficient D-optimal designs. This approach allows one to represent the support points of the designs by Taylor series, which gives us the opportunity to construct the designs by hand using tables of the coefficients of the series. Such tables are provided here for models with two nonlinear parameters. Furthermore, the recurrent formulas for constructing the tables for arbitrary numbers of parameters are introduced.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Nonlinear regression; Experimental designs; Maximin efficient designs; Functional approach; Exponential models; Rational models; D-Criterion; Taylor expansions; Implicit function theorem
Publisher:	Elsevier
ISSN:	0378-3758
Last Modified:	24 Oct 2022 11:42
URI:	https://orca.cardiff.ac.uk/id/eprint/49052

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