Optimal Characteristic Designs for Polynomial Models

  1. Rodríguez-Díaz, J. M. 1
  2. López-Fidalgo, J. 1
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

Libro:
Nonconvex Optimization and Its Applications

ISSN: 1571-568X

ISBN: 9781441948465

Año de publicación: 2001

Volumen: 51

Páginas: 123-130

Tipo: Capítulo de Libro

DOI: 10.1007/978-1-4757-3419-5_12 GOOGLE SCHOLAR

Resumen

Using the characteristic polynomial coefficients of the inverse of the informa-tion matrix, design criteria can be defined between A-and D-optimality (Lopez-Fidalgo and Rodriguez-Diaz, 1998). With a slight modification of the classical algorithms, the gradient expression allows us to find some optimal characteristic designs for polynomial regression. We observe that these designs are a smooth transition from A-to D-optimal designs. Moreover, for some of these optimal designs, the efficiencies for both criteria, A-and D-optimality, are quite good. Nice relationships emerge when plotting the support points of these optimal designs against the number of parameters of the model. In particular, following the ideas developed by Pukelsheim and Torsney (1991), we have considered A-optimality. Another mathematical expression can be given for finding A-optimal support points using nonlinear regression. This could be very useful for obtaining optimal designs for the other characteristic criteria.

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