Optimal minimax designs for prediction in heteroscedastic models |
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| Institution: | 1. Department of Pharmacy, National University of Singapore, Singapore;2. Division of Nephrology, Department of Medicine, National University Hospital, Singapore;3. Department of Dietetics, National University Hospital, Singapore;4. Department of Pharmacy, National University Hospital, Singapore;1. Department of Information Science and Engineering, PESIT-BSC, Bangalore, India;2. Department of Computer Science and Engineering, PESIT-BSC, Bangalore, India;3. Indian Institute of Astrophysics, Bangalore, India;4. Department of Physics, Center for Post Graduate Studies, Jain University, Bangalore, India;5. Visiting Associate IUCAA, Pune, India;6. Department of Computer Science and Information Systems, BITS, Hyderabad, India;1. School of Health Sciences, Universiti Sains Malaysia, 16150 Kubang Kerian, Kelantan, Malaysia;2. Departamento de Medicina Experimental, Facultad de Medicina Universidad Nacional Autónoma de México, 04510 México, D.F., Mexico;3. Institute for Research in Molecular Medicine, Universiti Sains Malaysia, 16150 Kubang Kerian, Kelantan, Malaysia;4. School of Medical Sciences, Universiti Sains Malaysia, 16150 Kubang Kerian, Kelantan, Malaysia;5. Institute for Research in Molecular Medicine, Universiti Sains Malaysia, 16150 Kubang Kerian, Kelantan, Malaysia;1. Division of Endoscopy, Department of Integrated Diagnostics & Therapeutics, National Taiwan University Hospital, National Taiwan University, Taipei, Taiwan;2. Department of Internal Medicine, College of Medicine, National Taiwan University, Taipei, Taiwan;3. Division of Gastroenterology and Hepatology, Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan;4. Department of Laboratory Medicine, National Taiwan University Hospital, National Taiwan University, Taipei, Taiwan;5. Department of Laboratory Medicine, College of Medicine, National Taiwan University, Taipei, Taiwan;6. Department of Pathology, National Taiwan University Hospital, National Taiwan University, Taipei, Taiwan;7. Division of Gastroenterology and Hepatology, Department of Internal Medicine, Chung Shan Medical University Hospital, Taichung, Taiwan;8. School of Medicine and Institute of Medicine, Chung Shan Medical University Hospital, Taichung, Taiwan |
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| Abstract: | We construct optimal designs for heteroscedastic models when the goal is to make efficient prediction over a compact interval. It is assumed that the point or points which are interesting to predict are not known before the experiment is run. Two minimax strategies for minimizing the maximum fitted variance and maximum predictive variance across the interval of interest are proposed and, optimal designs are found and compared. An algorithm for generating these designs is included. |
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