Properties of information matrices for linear models and universal optimality of experimental designs

✍ Scribed by Augustyn Markiewicz

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 500 KB
• Volume: 59
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00106-1

✦ Synopsis

Properties of information matrices for certain fixed effects models and for related mixed effects models are investigated. It is shown that a design which is universally optimal for estimating a given set of parameters under the fixed effects model is also universally optimal for estimating a reduced set of parameters under the fixed effects models as well as under the related mixed effects model. As an application, using the Kiefer ordering defined in Pukelsheim (Optimal Designs of Experiments (1993), Wiley, New York), general sufficient conditions for universal optimality are established. Some optimality results on repeated measurements designs of Cheng and Wu (Ann. Statist. 11 (1980), 349) and Mukhopadhyay and Saha (Cal. Statist. Assoc. Bull. 32 (1983), 153 168) are generalized.