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mODa 8 - Advances in Model-Oriented Design and Analysis pp 115–122Cite as

D-optimal Designs for Nonlinear Models Possessing a Chebyshev Property

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Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

The paper is devoted to experimental design for nonlinear regression models, whose derivatives with respect to parameters generate a generalized Chebyshev system. Most models of practical importance possess this property. In particular it is seen in exponential, rational and logistic models as well as splines with free knots. It is proved that support points of saturated locally D-optimal designs are monotonic and real analytic functions of initial values for those parameters on which models depend nonlinearly. This allows one to represent the functions by Taylor series. Similar properties of saturated maximin efficient designs are also investigated.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St.Petersburg State University, University avenue 28, Petrodvoretz, 198504, St. Petersburg, Russia

    Viatcheslav B. Melas

Authors
  1. Viatcheslav B. Melas
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Editor information

Editors and Affiliations

  1. Departamento de Matemáticas, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Avda. Camilo José Cela, 3, 13071, Ciudad Real, Spain

    Jesús López-Fidalgo

  2. Departamento de Estadística, Facultad de Ciencias, Universidad de Salamanca, Plaza de los Caídos s/n, 37008, Salamanca, Spain

    Juan Manuel Rodríguez-Díaz

  3. Department of Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW, UK

    Ben Torsney

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© 2007 Physica-Verlag Heidelberg

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Melas, V.B. (2007). D-optimal Designs for Nonlinear Models Possessing a Chebyshev Property. In: López-Fidalgo, J., Rodríguez-Díaz, J.M., Torsney, B. (eds) mODa 8 - Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1952-6_15

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