Minimum support invariant designs for multiple cubic regression

✍ Scribed by Norbert Gaffke; Berthold Heiligers

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 166 KB
• Volume: 72
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(98)00034-2

✦ Synopsis

The numerically optimal designs for cubic multiple regression on a ball (centered at the origin) are supported only by two spheres, one of which is the surface of the ball. However, their support sizes rapidly increase along with an increasing number of regressors. So a practically important problem is to ÿnd equivalent designs (i.e., designs sharing the same moment matrix) having a small support. The present paper solves this problem within a subclass of designs being invariant under the coordinate permutation and sign change transformation groups. We develop a procedure for obtaining a minimum support invariant design associated with the optimal moment matrix. Only a small number of competing designs have to be inspected, thus the procedure is numerically highly e cient.