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。

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.

目錄
第一章 導論	1
第一節 研究動機與文獻回顧	1
第二節 研究方法	4
第三節 研究架構	5
第二章 文獻探討	7
第一節 無母數迴歸估計	7
第二節 分量迴歸分析簡介	10
第三節 函數型係數分量迴歸簡介	12
第三章 半參數部分線性模型及其估計方法	14
第一節 半參數部分線性分量迴歸模型	14
第二節 Cai and Xiao (2012)的二步驟估計方法	15
第三節 Kai et al. (2011)的三步驟估計方法	17
第四節 函數型係數模型之檢定	19
第四章 模擬分析	29
第一節 模擬設定	29
第二節 模擬結果	30
第五章 結論	42
第一節 研究成果	42
第二節 討論及未來研究	42
參考文獻	44

表目錄 
表 1區域線性、NW及GM估計量, 三者的漸進偏誤及漸進變異數	9
表 2在不同迴歸點個數m與函數型係數個數下卡方表查表值α=0.05	23
表 3在不同迴歸點個數m與函數型係數個數下卡方表查表值α=0.1	26
表 4模擬500次β_1之ADE的中位數與ADE的標準差值	31
表 5模擬500次β_2之ADE的中位數與ADE的標準差值	32
表 6模擬500次α_1之MADE的中位數與MADE的標準差值	33
表 7模擬500次α_2之MADE的中位數與MADE的標準差值	34
表 8模擬500次α_3之MADE的中位數與MADE的標準差值	35
表 9在n為100和k為0.0125時不同迴歸點個數與分量下的檢定力值	37
表 10在n為100和k為0.025時不同迴歸點個數與分量下的檢定力值	37
表 11在n為100和k為0.05時不同迴歸點個數與分量下的檢定力值	38
表 12在n為200和k為0.0125時不同迴歸點個數與分量下的檢定力值	38
表 13在n為200和k為0.025時不同迴歸點個數與分量下的檢定力值	39
表 14在n為200和k為0.05時不同迴歸點個數與分量下的檢定力值	39
表 15在n為300和k為0.0125時不同迴歸點個數與分量下的檢定力值	40
表 16在n為300和k為0.025時不同迴歸點個數與分量下的檢定力值	40
表 17在n為300和k為0.05時不同迴歸點個數與分量下的檢定力值	41

圖目錄
圖 1 分量迴歸損失函數圖	11

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