96-20

Minimum Support Invariant Designs for Multiplle Cubic Regression

by Gaffke, N.; Heiligers, B.

 

Preprint series: 96-20, Preprints

The paper is published: Journal of statistical planning and inference, 72 (1998) \rS. 229-245

 

Abstract: The numerically optimal designs for cubic multiple regression on aball (centered at the origin) are supported only by two sheres one ofwhich is the surface of the ball. However, their support sizes increaserapidly when the number of regressors increases, So a practically im-portant problem is to find equivalent designs (i.e., designs sharing thesame information matrix) can be found which have a smaller support.The present paper solves this problem within the class of designs whichare invariant under the coordinate permutation and sign change trans-formation groups. We develop a procedure for obtaining a minimumsupport invariant design associated with the optimal moment matrix.Only a small number of competing designs have to be inspected, thusthe procedure is numerically highly efficient.


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