相關截切資料下存活函數估計之穩健性評估

Robustness Examination for The Survival Function Estimation under A Dependent Truncation

張珮嫚(Pei-Man Chang)

指導教授 ： 謝進見

國立中正大學/理學院/數學系統計科學研究所/碩士(2014年)

摘要

在這篇論文中,我們藉由大量的模擬研究檢驗 Lakhal,Rivest 和 Ab- dous (2006) 的穩健性表現。Lakhal,Rivest 和 Abdous (2006) 發表了 一個在相關截切下,估計相關性和存活函數的方法。由模擬的結果, 發現 Lakhal et al. (2006) 所提出的方法在一些情況下是不穩健的。而 且,在估計過程中會出現解根的問題。

關鍵字

穩健性 ； 截切相關性 ； Archimedean copula

並列摘要

In this thesis, we examine the robustness performance for Lakhal, Rivest and Abdous (2006) via large simulation studies. Lakhal et al. (2006) pro- posed an approach to estimate the association and the survival function under a dependent truncation. From the simulation results, it shows the performance of Lakhal et al. (2006) is not robust for some cases. Further, there is a problem for solving equations in their estimation procedure.

並列關鍵字

Robustness ； Dependent truncation ； Archimedean copula

參考文獻

[1] Genest, C., and Rivest, L. P. (1993). Statistical Inference Procedures for Bivariate Archimedean Copulas. J. Am. Statist. Assoc. 1993, Vol. 88, No. 423, 1034-1043.

[2] Genest, C., and Mackay, J. (1986). The Joy of Copulas: Bivariate Distributions with Uniform Marginals. Am. Statist. Assoc. 1986, Vol. 40, No. 4, 280-283.

[4] Lakhal, L., Rivest, L. P. and Abdous, B. (2008). Estimating Survival and Association in a Semicompeting Risks Model. Biometrics 64, 180-188.

[5] Lakhal, L., Rivest, L. P. (2006). Estimating Survival Under a De- pendent Truncation. Biometrika 93, 655-669.

[6] Oakes, D. (1989). Bivariate Survival Models Induced by Frailties. J. Am. Statist. Assoc. 1989, Vol. 84, No. 406, 487-493.