- 學位論文
存活右設限和現狀數據混合資料之分佈函數估計
Distribution function estimation for mixed right-censored and current status data
摘要
存活分析是醫學和電子業上一個相當重要的研究。研究存活分析首當就是從最簡單的右設限資料和現狀數據研究起，而本論文就是在研究右設限和現狀數據混合資料時的分佈函數之估計，我們的模型是利用伯氏多項式來描述分佈函數，其估計方法則採用最大概似估計，因為伯氏多項式的參數較為複雜，我們將用馬可夫鏈蒙地卡羅法來進行計算估計，而本論文提供了三種演算法：(一) 遞增之演算法；(二) 凹口向上且遞增之演算法；(三) Simulated Annealing演算法，我們取其中的兩種演算法進行模擬計算和比較。若我們知道，當真實的分佈函數的圖形是凹口向上的時候，我們利用凹口向上且遞增之演算法會估得比較好。但是不管如何，當資料愈大時，兩種演算法都估的很準確。這些模擬的數據，皆呈現在論文當中，也符合了大樣本性質的理論，因此，我們對此研究方法相當滿意。
並列摘要
Survival analysis is a very important study for medicine and electronics industry. First, survival analysis stars from the simplest right-censored and current status data. This thesis aims at distribution function estimation for mixed right-censored and current status data. Our model uses Bernstein polynomial to describe the distribution function, and maximum likelihood method is used to estimate. Because the parameters of Bernstein polynomial are more complex, we use Markov chain Monte Carlo method to calculate the estimated. This thesis provides three algorithms, (a) Algorithm increments, (b) Notch upward and increasing the algorithm, and (c) Simulated Annealing algorithm. And then we take two of these algorithms to simulate and compare. If the graph notch of the distribution function is up, it’s better to use Notch upward and increasing the algorithm to estimate. But no matter how, when the data is larger, both estimates of algorithms are very accurate. These simulated data, which are present in this thesis, are also conformed the nature of the large sample theory. Therefore, we were satisfied with this methodology.