近年來，地理加權迴歸(GeographicallyWeighted Regression; GWR; Brunsdon et al., 1998) 已成為各領域中探討空間異質性時不可或缺的空間資料分析方法之一；而分量迴歸(Quantile Regression; QR) 由於可估計反應變數的百分位數，其應用性亦備受注意。為了增加空間資料分析的彈性, Chen et al. (2012) 將這兩種方法做結合，並提出了地理加權分量迴歸(Geographically Weighted Quantile Regression; GWQR)。地理加權分量迴歸方法雖可有效的探索各地方解釋變數與反應變數各分量在空間上的變化情形，但卻未能將空間相依性(spatial autocorrelation)也考慮於模式中。本研究的目的是利用工具變數(instrumental variable)的手法，將空間自相關模式(spatial autoregression model) 的想法導入，以拓展可同時探討空間異質性與空間局部自相關(Spatial Local Autocorrelation) 效應的地理加權自相關分量迴歸模式(Geographically Weighted Autoregressive Quantile Regression; GWAQR)。本研究使用蒙地卡羅模擬, 檢驗該模式參數估計量的表現情形，並根據結果提供研究者在不同樣本數的情況下使用此模式的準則。

Geographically Weighted Regression (GWR; Brunsdon et al., 1998) and Quantile Regression (QR; Koenker and Bassett, 1978) are two important tools respectively in geography and econometrics in analyzing various issues of empirical studies. The former is designed to explore spatial nonstationarity and the latter is constructed to model relationships among variables across the whole distribution of a dependent variable. While both of these methods have been widely used in literature, they seem to be two unconnected lines of knowledge inquiry until recently (Chen et al., 2012). Chen et al. developed an approach so-called GeographicallyWeighted Quantile Regression (GWQR) to integrate QR and GWR. This innovative approach can explore the spatial nonstationarity not only over space but also across different levels of the dependent variable. It is, however, argued as a methodological issue that the GWQR does not account for spatial dependence between geographic locations. The goal of this study is then to address such perceived gap, and to introduce a Geographically Weighted Autoregressive Quantile Regression (GWAQR) model which includes (local) spatial lag autocorrelation components. A simulation study is conducted as well to examine the performance of the proposed estimator and further validate the GWAQR methodology.

目錄
第一章緒論............................ ............................ 1
1.1 研究背景.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.2 研究動機與目的.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10
1.3 研究架構.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 12
第二章文獻探討...................... ............................ 13
2.1 分量迴歸.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 13
2.2 地理加權迴歸.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 15
2.2.1 估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 核函數與帶寬的選擇. . . . . . . . . . . . . . . . . . . . 18
2.3 地理加權分量迴歸.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 21
第三章研究方法...................... ............................ 26
3.1 空間自迴歸模式.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 26
3.2 地理加權自相關分量迴歸模式.. .. .. .. .. .. .. .. .. .. .. .. .. .. 32
3.3 參數估計.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 33
3.4 選擇帶寬.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 37
3.5 參數之標準誤.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 38
3.6 工具變數的選擇.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 40
第四章模擬分析...................... ............................ 43
4.1 模擬設定.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 43
4.2 模擬結果.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 46
4.3 喬治亞州座標之模擬研究.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 55
第五章結論............................ ............................ 57
5.1 研究成果.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 57
5.2 討論及未來研究.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 58
參考文獻.............................. ............................ 59

圖目錄
1.1 教育程度對於家庭收入的條件平均與條件分量之影響. . . . . . . 2
1.2 1991年倫敦公寓與連棟住宅的房屋坪數對房屋售價之影響(係數估
計值) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 1991年倫敦公寓與連棟住宅房屋坪數迴歸係數估計量之比例. . . 6
1.4 1991年倫敦公寓與連棟住宅的房屋坪數對房屋售價之影響. . . . 8
1.5 傳統平均數迴歸與地理加權迴歸之比較(考慮空間非平穩現象) . . . 9
2.1 核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 固定核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 適應核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 鄰近矩陣中判斷鄰近地區的3種方式. . . . . . . . . . . . . . . . 29
3.2 距離矩陣中判斷鄰近地區的2種方式. . . . . . . . . . . . . . . . 31

表目錄
4.1 使用不同工具變數時地理加權自相關分量迴歸模式之空間延遲係數
與迴歸係數誤差平均數與中位數. . . . . . . . . . . . . . . . . . 49
4.2 使用不同工具變數時地理加權自相關分量迴歸模式之空間延遲係數
與迴歸係數平方誤差的平均數與平方誤差的中位數. . . . . . . . 50
4.3 使用不同工具變數時地理加權自相關分量迴歸模式之空間延遲係數
與迴歸係數的均方根誤差. . . . . . . . . . . . . . . . . . . . . . 53
4.4 使用不同工具變數時地理加權自相關分量迴歸模式之均方根預測誤差54
4.5 使用不同工具變數時地理加權自相關分量迴歸模式之空間延遲係數
與迴歸係數誤差平均數與中位數(喬治亞州實際座標) . . . . . . . 56

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