設限資料下分量迴歸模型分析之文獻回顧

Quantile Regression Analysis based on Censored Data A Literature Review

林欣穎(Hsin-Ying Lin)

指導教授 ： 王維菁

國立交通大學/理學院/統計學研究所/碩士(2011年)

https://doi.org/10.6842/NCTU.2011.00142

摘要

在此論文中，我們回顧分量迴歸模型的重要文獻。首先，我們介紹在沒有變數之完整資料下，估計分量的推論技巧，藉此了解分量的幾何結構和分析上問題的困難處。接著，我們引進變數的影響和討論不同的估計程序，並提供幾何上的解釋意義。最後，我們加入設限的影響並且討論幾種修正的估計方法。我們提供系統化的架構，讓讀者透過推論方法基本的建構原則，對分量迴歸模型有初步的了解。

關鍵字

分量迴歸模型 ； 設限

並列摘要

In the thesis, we review important literature on quantile regression models for survival data. First, we introduce the inference techniques for estimating a quantile based on complete data without covariates. This allows us to see the geometric structure and analytical difficulty of the problem. Then we include the effect of covariates and discuss different estimation procedures. Geometric explanations are also provided. Finally the effect of censoring is incorporated and we discuss several approaches of modification. We aim to provide a systematic framework which allows the readers to understand the quantile regression model from fundamental inference principles.

並列關鍵字

Quantile regression model ； Censoring

參考文獻

[1] Barrodale, I., and Roberts, F. D. K. (1974), “Solution of an Overdetermined System of Equations in the Norm,” Communications of the ACM, 17, 319-320.

[2] Honoré, B., Khan, S., and Powell J. L. (2002), “Quantile Regression Under Random Censoring,” Journal of Econometrics, 109, 67-105.

[3] Lin, D.Y., and Geyer, C. J. (1992), “Computational Methods for Semiparametric Linear Regression with Censored Data,” Journal of Computational and graphical Statistics, 1, 77-90.

[4] Necleous, T., Branden, K. V., and Portnoy, S. (2006), “Correction to Censored Regression Quantiles by S. Portnoy, 98 (2003), 1001-1012,” Journal of the American Statistical Association, 101, 869-861.

[5] Peng, L., and Huang, Y. (2008), “Survival Analysis with Quantile Regression Models,” Journal of the American Statistical Association, 103, 637-649.