Copula模型假設下之分量迴歸分析

Copula-based quantile regression analysis

翁澤群(Ze-Qun Weng)

指導教授 ： 王維菁

國立交通大學/理學院/統計學研究所/碩士(2020年)

摘要

在此論文中，我們回顧了關於copula迴歸模型的重要文獻，並且提出了一種直觀的方法，用於估計右設限資料的條件分量。論文的主要思路是將分量迴歸函數用copula函數和邊際分佈函數表示，並據此建立一個估計式。在分別以母數和無母數的方式估計copula和邊際分佈函數之後，使用plug-in的方法來估計估計迴歸函數。我們還討論了多變量情況下的copula模型選擇，以避免模型錯誤指定帶來的問題。此外，我們透過模擬檢驗我們所提出的估計量在有限樣本下的表現。最後我們用所提出的方法分析了一筆心臟移植的真實資料。

關鍵字

Copula ； 分量回歸 ； 設限 ； 半母數估計

並列摘要

This thesis reviews the important literature about copula-based regression and proposes a new intuitive approach to estimate the conditional quantile for right censored data. The main idea presented in this thesis is to set up an estimation equation by rewriting the quantile regression function as copula and marginal functions. The plug-in method is used to estimate the regression function after the copula and marginals are estimated parametrically and nonparametrically respectively. We also discuss the selection of copula models in multivariate cases to avoid the problem brought by model misspecification. Furthermore, we provide simulations to assess our estimator. Finally, we analyze a real dataset of heart transplantation with our estimation method.

並列關鍵字

Copula ； Quantile regression ； Censoring ； Semiparametric

參考文獻

[10] Bedford, T., Cooke, R.M. “Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines”, Annals of Mathematics and Artificial Intelligence 32, 245–268 (2001). https://doi.org/10.1023/A:1016725902970.

[1] Sklar, A. (1959). “Fonctions de répartition à n dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris, 8, 229–231.

[2] Adham, S. A., Abd Elaal, M. K., and Malaka, H. M. (2016). “Gaussian copula regression application”, Journal International Mathematical Forum,11, 1053-1065.

[3] Hsin-Ying Lin. “Quantile Regression Analysis based on Censored Data -A Literature Review”, Degree of Master, May 2012.

[4] Hohsuk Noh, Anouar El Ghouch & Taoufik Bouezmarni (2013). “Copula-Based Regression Estimation and Inference”, Journal of the American Statistical Association, 108: 502,676-688.