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論文名稱 Title |
加權多項式迴歸之A 最適設計 A-optimal designs for weighted polynomial regression |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
20 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2005-05-26 |
繳交日期 Date of Submission |
2005-07-05 |
關鍵字 Keywords |
Remez交換演算法、遞迴演算法、加權多項式迴歸、隱函式定理、A-等價定理、A-最適設計、泰勒展開式 A-Equivalence Theorem, recursive algorithm, Taylor expansion, A-optimal design, Remez's exchange procedure, implicit function theorem, weighted polynomial regression |
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統計 Statistics |
本論文已被瀏覽 5723 次,被下載 1822 次 The thesis/dissertation has been browsed 5723 times, has been downloaded 1822 times. |
中文摘要 |
這篇文章主要是研究在區間 [m-a, m+a],具有可解析加權函式多項式迴歸的A-最適設問題。當a是趨近於0時,此最適設計的結構僅決於a和加權函式。此外,假如此加權函式在a=0時是可解析函式,則一個伸縮的最適設計點和權重a=0時是可解析函式。利用泰勒展開式係數可以決定一個遞迴公式來計算A-最適設計。 |
Abstract |
This paper is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m-a,m+a]. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points and weights is analytic functions of a at $a=0$. We make use of a Taylor expansion which coefficients can be determined recursively, for calculating the A-optimal designs. |
目次 Table of Contents |
Contents Abstract . . . . . . . . . . . . . . . . . . . . . . ii 1. Introduction . . . . . . . . . . . . . . . . . . . 1 2. Preliminary . . .. . . . . . . . . . . . . . . . . 2 3. Taylor expansion for A-optimal designs . . . . . . . . . . . . . . . . . . . . . . . 5 4. Example . . . . . . . . . . . . . . . . . . . . . 7 5. Conclusions . . . . . . .. . . . . . . . . . . . . 8 Appendix . . . . . . . . . . . . . . . . . . . . . . 10 References . . . . . . . . . . . . . . . . . . . . . 12 |
參考文獻 References |
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