空間統計學中，如何透過有限的抽樣點資料對未抽樣的位置進行空間預測是感興趣且重要的議題。不同於一般的固定係數空間迴歸模型，本文透過平滑樣條(smoothing splines)函數提出變異係數空間迴歸模型。模型中，我們考慮迴歸係數可隨地理位置變化並設計二階段的演算法估計迴歸係數曲面及模型參數，進而得到研究區域的空間預測曲面。本文亦透過統計假設檢定，讓資料自動決定該使用變異係數或固定係數的空間迴歸模型。完整的數值模擬實驗呈現並比較兩種空間預測方法的表現，同時也藉由分析臺灣PM2.5濃度的數據說明所提方法的實用性。

In spatial statistics, how to make spatial prediction for unsampled locations based on observed noisy data is an interesting and important issue. Different from general spatial regression models with fixed regression coefficients, this thesis proposes a spatially varying coefficient regression model via a smoothing spline technique, where the regression coefficients are allowed to vary with geographic locations. A two-stage algorithm is designed to estimate regression coefficients as well as model parameters. Then, a predicted surface over the study region can be obtained. In practice, how to determine an appropriate method between the varying coefficient model and the fixed coefficient model is another important issue which can be solved by a statistical hypothesis test. Numerical results show the effectiveness of the proposed methodology and a real data example regarding the fine particulate matter (PM2.5) concentration in Taiwan is analyzed for illustration.

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