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; PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |