A Study on Criterion-Robust Optimal Designs for Model Discrimination and Parameter Estimation

• Main Authors: Min-Hsiao Tsai, 蔡旻曉
• Other Authors: Mei-Mei Zen
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/34225885476318317456

博士 === 國立成功大學 === 統計學系碩博士班 === 91 === Consider the problem of discriminating between two rival polynomial regression models on the q-cube [-1,1]^q, qεN, or two rival Fourier regression models on the circle [-π,π], and estimating parameters in the models. In order to find experimental designs which are efficient for both purposes of model discrimination and parameter estimation simultaneously, we propose a general multiple-objective optimality criterion, Mr-optimality criterion, which is a weighted geometric average of D- and Ds-efficiencies, it puts weight r (0≦r≦1) for model discrimination and (1-r) for parameter estimation. The corresponding Mr-optimal design is explicitly derived in terms of canonical moments. Moreover, the behavior of the proposed Mr-optimal designs is investigated under different weighted selection criterion. Furthermore, applying the maximin principle on the efficiencies of experimental designs, the extreme value of the minimum Mr-efficiency of any Mr''-optimal design is obtained at r''=r*, which results in the corresponding Mr*-optimal design to be served as a criterion- robust optimal design for the described problem.