A Note on Criterion-Robust Optimal Designs for Model Discrimination and Parameter Estimation in Polynomial Regression Models |
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Authors: | Mei-Mei Zen Chia-Hao Chan Yi-Hsiung Lin |
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Institution: | 1. Department of Statistics , National Cheng-Kung University , Taiwan , R.O.C. mmzen@stat.ncku.edu.tw;3. Department of Statistics , National Cheng-Kung University , Taiwan , R.O.C. |
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Abstract: | Consider the problem of discriminating between the polynomial regression models on ?1, 1] and estimating parameters in the models. Zen and Tsai (2002
Zen , M. M. ,
Tsai , M. H. ( 2002 ). Some criterion-robust optimal designs for the dual problem of model discrimination and parameter estimation . Sankhya Ind. J. Statist. 64 : (Series B, Pt. 3) : 322 – 338 . Google Scholar]) proposed a multiple-objective optimality criterion, M γ-criterion, which uses weight γ (0 ≤ γ ≤ 1) for model discrimination and α = β = (1 ? γ)/2 for parameter estimation in each model. In this article, we generalize it to a wider setup with different values of α and β. For instance, α = 2 β suggests that the “smaller” model is more likely to be the true model. Using similar techniques, the corresponding criterion-robust optimal design is investigated. A study for the original criterion-robust optimal design with α = β, through M-efficiency, shows that it is good enough for any wider setup. |
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Keywords: | Canonical moments Efficiency M γ m *-optimal design Multiple-objective Selection criterion |
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