具函數型係數的部分線性分量迴歸模型之研究

A study of the partially linear quantile regression model with smooth coefficients

周世桓(Shih-Huan Chou)

指導教授 ： 鄧文舜

淡江大學/商管學院/統計學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00822

摘要

分量迴歸(quantile regression)是一種探討解釋變數與反應變數的分量(response quantile)之函數關係的統計方法, 近年來, 己有許多學者將傳統的平均數迴歸(mean regression)中所使用的半參數(semiparametric)迴歸模式, 引入分量迴歸模式中, 建構所謂的半參數分量迴歸模式, 在諸多的半參數分量迴歸模式中, 目前最廣義且最有應用價值的可以說是部分線性變動係數(partially linear varying coefficient)分量迴歸模式, 此一迴歸模型中的部分解釋變數具有函數型係數, 並且部分解釋變數的迴歸係數, 則為固定常數, 在本文中, 我們探討並比較Cai and Xiao (2012)以及Kai et al. (2011)二種的核估計(kernel estimation)方法。根據模擬研究顯示, 兩種估計方法下的估計量, 其估計效果並無顯著差異。 另外Cai and Xiao (2012)所提出一種卡方法檢定, 來檢定是否若干迴歸係數為固定常數, 這個檢定必需事先選定迴歸點的個數(number of regression points), 本文進行一項模擬研究, 探討檢定力和迴歸點個數之間的關係, 結果發現檢定力會先隨著迴歸點的個數增加而增加, 但增加到一定程度之後, 又隨之遞減。最後, 為方便使用者進行Cai and Xiao (2012)的卡方檢定, 我們用數值方法計算出若干型一誤差下的顯著點(significance points), 並製成表, 供查表之用。

關鍵字

分量迴歸 ； 變動係數迴歸 ； 半參數迴歸 ； 半參數分量迴歸 ； 核函數估平滑法

並列摘要

Quantile regression is a statistical method to analysis the associations between the explanatory variables and the quantile of the response variable. Recently, many researchers have proposed semiparametric quantile regression regression model that have been well developed in the context of classical mean regression model. Among the various semiparametric quantile regression model, the partially linear smooth coefficient quantile regression model is the most general and useful quartile regression method. In this dissertation, we shall investigate and compare the kernel estimation methods of Cai and Xiao (2012) and Kai et al. (2011) through a variety of simulation studies. The results show that two kernel estimation methods have similar performances. Cai and Xiao (2012) propose a chi-square test to detect whether a set of coefficients are fixed constant. Their test depends on the number of regression points chosen by the investigator. The simulation studies show that the power performance improves as the number of regression points grows but deteriorates as it grows further. Finally, we provide a chi square table for some significance levels to enable the use of Cai and Xiao’s test.

並列關鍵字

quantile regression ； varying coefficient regression ； semiparametric regression ； semiparametric quantile regression ； kernel estimation method

參考文獻

Ahmad, I., Leelahanon, S. and Li, Q. (2005). Efficient estimation of a semiparametric partiallylinear varying coefficient model. The Annals of Statistics, 33, 258-283.

Buchinsky, M. (1998). Recent advances in quantile regression models: a practical guide forempirical research. Journal of Human Resources, 33, 88-126.

Cade, B. and Noon, B. (2003). A gentle introduction to quantile regression for ecologists.Front Ecol Environ 1, 412-420.

Cai, X. and Xu, X. (2008). Nonparametric quantile estimations for dynamic smoothcoefficient models. Journal of the American Statistical Association, 103, 1596-1608.

Cai, X. and Xiao, Z. (2012). Semiparametric quantile regression estimation in dynamic modelswith partially varying coefficients. Journal of Econometrics, 167, 413-425.