設限資料在半參數線性轉換模型之下的核函數估計

Semiparametric Linear Transformation Model with Kernel Density Estimation

林韋君(Wei-Chun Lin)

指導教授 ： 陳蔓樺

淡江大學/商管學院/統計學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00525

摘要

線性轉換模型為一個相當彈性的半參數迴歸模型。在存活分析中，最常被使用在分析上的比例風險模型以及比例勝算模型皆為線性轉換模型的兩個特例。因此，本篇研究將探討在線性轉換模型之下，利用核密度估計方法對未知累加基底風險函數進行估計的表現。本篇選用Nadaraya-Watson核估計量對半參數迴歸模型中非參數的部分進行估計。參數部分利用Newton-Raphson方法進行估計。
在本篇中，將核密度估計方法應用在不同分配之下的估計。並且比較不同帶寬、核函數的選擇對估計結果的影響。而在模擬研究中，假設未知累加基底風險函數服從韋伯分配，利用核密度估計方法估計出來的結果顯示，只要樣本數夠大，估計的表現較好。此外，核密度估計結果的好壞，與帶寬的選擇有密切的關係。

關鍵字

線性轉換模型 ； 核密度估計 ； 設限資料

並列摘要

In survival analysis, the most commonly used models, the proportional hazard model and the proportional odds model, are special cases of linear transformation model. Because of its flexibility, our aim in this thesis is to explore the performance of kernel density estimation on unknown baseline cumulative hazard function under linear transformation model. In this thesis, we chose Nadaraya-Watson kernel estimator to estimate the nonparametric part of linear transformation model. Then we used Newton-Raphson method in the estimation of parametric part, and obtained the estimate of parameter which we are interested in.
We presented the application of kernel density estimation on different functions with different kernel functions and bandwidths. In simulation studies, we assume the baseline cumulative hazard function followed a Weibull distribution, and found that the result of kernel density estimation under different censored rate performed well when the sample size is large. We also found that the choice of bandwidth plays an important role in kernel estimation.

並列關鍵字

Transformation Model ； Kernel Density Estimation ； Censored Data

參考文獻

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