Vol. LXXVII, 2 (2008)
p. 155 - 166

Computing the minimal efficiency of designs by a differentiable approximation of FEk-optimality criteria

L. Bušová

Received: May 9, 2005;  Revised: February 22, 2008;  Accepted: February 29, 2008

Abstract.  Consider the linear regression model with uncorrelated errors and an experimental design x. In the paper, we propose a numerical method for calculating the minimal efficiency of x in the class O of orthogonally invariant information criteria. For this purpose, we introduce the concept of Fk,p(m)-optimality criteria. Then we show that FEk(m) criteria can be differentiably approximated by Fk,p(m) criteria, therefore allowing us to use standard numerical procedures to arrive at boundaries for Fk,p(m) optimal values, and hence at the intervals for the minimal efficiency of designs under the class of all orthogonally invariant information criteria. The approach is then illustrated on the polynomial model of degrees 2, . . . ,8.

AMS Subject classification: Primary: 62K05;

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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