近幾年在部分圓上低階三角迴歸模型的各式各樣連續型的設計問題已被解決。在此篇論文中將討論：在部分圓上沒有截距項的一階三角迴歸模型的正合和連續D最適設計。藉由幾何的方法找尋出三角動差集合的邊界，且推導出邊界上設計的特徵，更藉此完整地提供正合D最適設計的解。我們發現，設計區間的長短和觀測點的 個數會影響正合D最適設計的解。

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 complete 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.

Acknowledgements i
Abstract ii
1 Introduction 1
2 Approximate D-optimal designs 3
3 The moment set of exact designs 5
4 Exact D-optimal designs 13
Appendix 15
References 20

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