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    Title: 使用伯氏多項式估計存活風險率
    Other Titles: Estimation for survival hazard rate using bernstein polynomials
    Authors: 郭育成;Kuo, Yu-cheng
    Contributors: 淡江大學數學學系碩士班
    溫啓仲;Wen, Chi-chung
    Keywords: 右設限資料;伯氏多項式;尼爾生-艾倫;最大概然估計;Right Censored Data;Bernstein Polynomial;Nelson- Aalen;Maximum Likelihood Estimator
    Date: 2008
    Issue Date: 2010-01-11 02:55:56 (UTC+8)
    Abstract: 本研究將根據右設限資料提出一個具平滑性質之存活風險率,而風險率模型所引進之參數將以最大概似估計法來估計。此估計程序可以提供一個存活風險率的平滑估計。我們根據牛頓法的原理,提出一個有效求取最大概似估計量的演算法。此估計方法的成功,於模擬試驗及對白血病患緩解時間的數據資料之分析結果將被說明。另外,我們的方法與尼爾生-艾倫方法的比較,和伯氏多項式階數之選取亦為本文討論的議題。
    In this thesis, we study the maximum likelihood estimator for a survival hazard rate with right censored data, in which the hazard rate is specified by the Bernstein polynomial. Our estimation procedure can provide a smooth estimator of the survival hazard rate. We develop an efficient Newton-Raphson based algorithm for the computation of the maximum likelihood estimate. The success of this method is demonstrated in simulation studies and in the analysis of Leukemia remission-time data. In addition, the comparison with Nelson-Aalen method is presented and the selection of the degree for Bernstein polynomial is discussed.
    Appears in Collections:[數學學系暨研究所] 學位論文

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