Exact D-optimal designs for first-order trigonometric regression models on a partial circle |
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Authors: | Fu-Chuen Chang Lorens Imhof Yi-Ying Sun |
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Institution: | 1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan, ROC 2. Department of Statistics and Hausdorff Center for Mathematics, Bonn University, 53113, Bonn, Germany
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Abstract: | Recently, various approximate design problems for low-degree trigonometric regression models on a partial circle have been solved. In this paper we consider approximate and exact optimal design problems for first-order trigonometric regression models without intercept on a partial circle. We investigate the intricate geometry of the non-convex exact trigonometric moment set and provide characterizations of its boundary. Building on these results we obtain a solution of the exact $D$ -optimal design problem. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of observations. |
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