本論文討論空間隨機效應模式之MLE參數估計，MLE可透過EM演算法有效率運算數值解。此研究同時也考量以lasso的技巧在模型的相關參數上做適度的規範，以達到簡化模型結構的目的。模擬結果驗證所提出之方法在不同模式下都有不錯的估計表現和預測表現。此外實例分析使用東海葉綠素濃度資料，利用提出的方法建立模式後，驗證有良好的預測表現，表示提出的方法可以應用在真實資料分析上。

關鍵字：fixed rank kriging、MLE方法、EM演算法、graphical lasso

The thesis is about the maximum likelihood estimation for spatial random effects model. The maximum likelihood estimation has no closed form but the numerical solution can be effectively solved through the EM algorithm. Moreover, some regularization methods for covariance parameters are incorporated in the estimation procedure to further simplify the fitted model structure. The simulation results verify that the proposed estimation methods have good performance in both estimation and prediction under various non-stationary models. The methodology is also applied to a real data set, chlorophyll concentration data from SeaWiFS projects, for illustration.

Keywords : fixed rank kriging, MLE, EM algorithm, graphical lasso

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