Equivalence theorems for compound design problems with application in mixed models

2020/07/29 by Maryna Prus, Prus, Maryna
Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Manufacturing Process and Optimization #Methodology (stat.ME) #Optimal Experimental Design Methods #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2007.14971

openalex publication_date 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on moment matrices (if criteria depend on designs via moment matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to the multiple-group random coefficient regression models and illustrate the results by simple examples.

Related

• Comparing robustness properties of optimal designs under standard and compound criteria
• Constructing K-optimal designs for different Scheffé models
• R-optimal designs for multi-response regression models with\n multi-factors
• T-optimal designs for multi-factor polynomial regression models via a semidefinite relaxation method
• Computing optimal experimental designs with respect to a compound Bayes\n risk criterion