存活右設限資料下風險函數之最大概似估計

Maximum Likelihood Estimator of Hazard Function for Right Censor Data

吳基溢(Ji-Yi Wu)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2011年)

https://doi.org/10.6840/CYCU.2011.00118

摘要

本論文, 對右設限資料用伯氏多項式來描述風險函數, 並且用最大概似估計來估計風險函數, 不同於丘真綺(2010) 也是用伯氏多項式來描述累積分配函數, 但其限制較多, 演算法較為複雜, 而我們在模擬研究中, 並和Kaplan-Meier 之方法,來
做比較, 我們在模擬研究比它們表現好, 並且在樣本越大時, 估計函數會越接近真實的. 雖然我們沒有證明大樣本的性質, 但其模擬結果顯示我們的方法應是正確的.

關鍵字

馬可夫鏈蒙地卡羅 ； 最大概似估計 ； 伯氏多項式 ； 風險函數

並列摘要

In the prsent study, the experimentor address the right censored data with Bernstein polynomial to describe the risk function and use maximum likelihood to estimate it. In Chiou (2010), who also described cumlative distribution function with Bernstein polynomial, her study displayed more restriction and complicted algorithm. However, in the simulation of the present study, the experimentor compares his way with Kaplan-Meier’s method. It shows that the estimated funciton will be more realistic when there are more samples. Though the experimentor don’t discusss the property of the larger sample size, the simulation can
still be correct to certify the hypothesis of the present study.

並列關鍵字

Hazard Function ； Markov Chain Monte Carlo ； Maximum Likelihood Estimator ； Bernstein Polynomial

參考文獻

[1] 丘真綺(2010). Maximum Likelihood Estimator of Using Bernstein Polynomial for Right Censor Data. Department of Applied Mathematics, Chung Yuan Christian University, master thesis .

[2] Chang, I. S., Hsiung, C. A., Wu, Y. J. and Yang, C. C. (2005). Bayesian survival analysis using Bernstein polynomials.Scandinavian Journal of Statistics 32, 447-466.

[3] Green, P. G. (1995). Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination.Biometrika 82, 711-732.

[4] Van Der Vart, A. W. & Wellner, J. A. (1996). Weak convergence and empirical processes. Springer-Verlag, New York.

[6] Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods. Springer-Verlag, New York.