本研究旨在建立一個非平穩空間模型(non-stationary spatial model) 來分析美國俄亥俄州各郡白人肺癌死亡人數資料於空間的分布現象，該模型中包含基底函數(basis function)及平穩過程(stationary process)。針對模型中所需估計的大量參數，我們使用Tibshirani (1996) 提出的最小絕對壓縮與篩選運算法(least absolute shrinkage and selection operator, lasso)，該方法可以幫助我們在估計參數的同時篩選變數，達到選模與建模的目的。結合Efron et al. (2004) 提出的最小角迴歸法(least angle regression, lars)，能夠加快估計法的計算速度，本研究使用R 軟體中的lars 套件來進行計算，我們也會使用交叉驗證法(cross-validation, cv)，幫助我們選擇lasso中最佳的調整參數(tunning parameter)。我們將估計結果繪製成空間分布圖，透過空間分布圖討論因肺癌死亡人數在空間上的關係。從分析結果中我們發現，在馬霍寧郡(Mahoning)、凱霍加郡(Cuyahoga)、盧卡斯郡(Lucas)、富蘭克林郡(Franklin)、蒙哥馬利郡(Montgomery) 及漢密爾頓郡(Hamilton) 的平均死亡人數較高，變異程度也較高；男性的肺癌死亡人數在俄亥俄州西南部的柯林頓郡(Clinton) 及高地郡(Highland)附近有較低相關性，而女性則在中部偏東的科肖克頓郡(Coshocton)附近有較低相關性。

In this research, we use a non-stationary spatial model to construct the distribution of the lung cancer data in Ohio. The model includes some basis functions and stationary processes. The least absolute shrinkage and selection operator (lasso) is used to estimate the parameters. The method of lasso can get the results of model selection and  parameter estimation simultaneously. We use the lars package in R language to solve the lasso estimation more efficiently. Cross-validation (cv) is used to choose the tunning parameter of lasso. We use the plots to show the distribution of the lung cancer data. Mahoning, Cuyahoga, Lucas, Franklin and Hamiltonthe have the higher average numbers and the variances of deaths. For male white people, the correlation of the average number of deaths is lower in Clinton and Highland. For female white people, the correlation of the average number of deaths is lower in Coshocton.

目錄
第一章簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第二章模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第三章估計方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
第一節最小絕對壓縮與篩選運算法(lasso) . . . . . . . . . . . . . . . . . . . 8
第二節交叉驗證法(cv) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
第三節本研究之估計方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第四章俄亥俄州肺癌資料之應用. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
圖目錄
3.1 交叉驗證法示意圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 俄亥俄州各郡地圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 各郡平均總人口數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 交叉驗證法結果圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 肺癌致死平均人數估計. . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.5 肺癌致死人數標準差估計. . . . . . . . . . . . . . . . . . . . . . . . 19
4.6 馬霍寧郡、凱霍加郡、盧卡斯郡、富蘭克林郡、蒙哥馬利郡、漢密
爾頓郡男性肺癌死亡人數的相關係數. . . . . . . . . . . . . . . . . . 22
4.7 馬霍寧郡、凱霍加郡、盧卡斯郡、富蘭克林郡、蒙哥馬利郡、漢密
爾頓郡女性肺癌死亡人數的相關係數. . . . . . . . . . . . . . . . . . 23
表目錄
4.1 男性平均肺癌死亡人數參數估計. . . . . . . . . . . . . . . . . . . . 17
4.2 女性平均肺癌死亡人數參數估計. . . . . . . . . . . . . . . . . . . . 18
4.3 男性肺癌死亡人數共變異數參數估計. . . . . . . . . . . . . . . . . . 20
4.4 女性肺癌死亡人數共變異數參數估計. . . . . . . . . . . . . . . . . . 20

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