在空間迴歸分析中，固定效應與隨機效應的混淆(相關) 會導致迴歸係數估計的偏差。本文提出一種新方法，利用固定秩克里金法(Fixed rank kriging) 來減少迴歸係數估計的偏差。此方法的一大優勢在於不需對反應變量的共變異數結構進行參數化假設，從而提高其實用性。在估計過程中，藉由選擇基底函數的數量來權衡估計量的偏差與變異。因此，為了進一步降低迴歸係數估計量的均方誤差，我們提出了Bagging 估計法和γ-估計法兩種策略。本文透過理論的探討驗證所提出估計量的特性。在模擬實驗的 部分，我們設計不同程度的空間混淆效應和各式的空間相關結構（如平穩、非平穩、等向和異向）進行測試，驗證所提方法的穩健性。最後，我們將此估計法應用於科羅拉多州降雨數據的案例用以呈現所提方法的實用性。;In spatial regression analysis, the confounding between fixed and random effects can lead to biased estimation of regression coefficients. This thesis proposes a novel estimation methodology that leverages the fixed rank kriging approach to mitigate these biases. A key advantage of the proposed method is that it circumvents the need for parametric assumptions about the covariance structure of the response variable, enhancing its practical applicability. The estimation process involves selecting an appropriate number of basis functions, which balances bias and variance in the estimators. To minimize the mean squared error of the estimators, we introduce two approaches: a bootstrap aggregation estimator and a γ-estimator. Theoretical properties of the proposed methodology are explored and justified. Extensive simulation studies under various spatial regression settings, including cases of spatial confounding and different correlation structures such as stationary, nonstationary, isotropic, and anisotropic, demonstrate the robustness of the proposed methods. Finally, the methodology is applied to a case study on precipitation data from Colorado, which highlights its practical effectiveness.
