在空間統計領域中，克利金（kriging）模型被廣泛應用於預測空間中感興趣的隨機變數，包括沒有觀測數據的位置。然而，這種預測方法依賴於空間相關函數的使用，而這些函數直接影響克利金預測結果的表現。本篇論文欲透過結合各種協方差函數於克利金空間模型中，探討空間相關函數對預測結果的影響。我們使用Kullback-Leibler 損失準則來評估克利金模型的表現，並透過數據擾動技術來估計和量化克里金模型的預測複雜性。基於此，我們提出了一個用於選擇適當協方差函數的準則。所提方法的有效性將透過多種模擬實驗驗證，並且我們將該方法應用於分析台灣的空氣品質數據，以說明其實用性。;In the field of spatial statistics, kriging models are frequently utilized for predicting variables of interest across a study region, including in areas without observational data, based on noise data observed at specific locations. The use of spatial correlation functions plays a crucial role in this context, as they directly impact the accuracy of kriging predictions. This thesis attempts to address this challenge by exploring the use of different covariance functions within spatial models. The performance of spatial kriging models employing various covariance functions is evaluated using the Kullback-Leibler loss criterion. Moreover, we measure the complexity of any spatial prediction method through the concept of generalized degrees of freedom, estimated using data perturbation techniques. Consequently, an estimated Kullback-Leibler loss criterion is proposed for selecting an appropriate covariance function. Focusing on spatial prediction, the effectiveness of the proposed method is validated through simulation experiments, and its practical utility is demonstrated using air quality data from Taiwan.
