迴歸分析是一種研究多個量化變數間關係的統計方法，尤其分量迴歸
(quantile regression) 是文獻上被廣泛使用方法之一，其概念為描述解釋變數在反應變數不同分量 (quantile) 上的影響效果。透過不同分量值，可將解釋變數對反應變數的影響更詳盡的呈現。本研究利用Zou and Yuan(2008)在假設所有分量下的迴歸係數(不包含截距項)\ 皆相等的情況下，所提出新的分量迴歸的估計方法 CQR (composite quantile regression)，在誤差分配 (error distribution) 不為常態分配下，其估計量的表現比 OLS (ordinary least square) 來得好。參考 CQR 的想法，我們試著將多個分量迴歸的聯合漸進分配，在與 CQR 相同假設下，經由多維常態分配得到的最大概似估計量，我們將此估計方法稱為 WQR (weighted quantile regression)。我們將 WQR 與過去的方法作 asymptotic relative efficiency 的比較，在誤差分配不為常態分配下表現最好，而從另一個研究發現，在有限樣本下 CQR 也能有很好的表現。在模擬分析方面考慮解釋變數過多的模型，所以也試著加入一些參數縮減方法作參考。最後整合上述的方法來探討台灣股市與美國股市有關連動性的實證分析。

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