本研究是根據Yuan[12]提出的Multi-resolution B-spline basis節點放置方法對於節點的篩選做進一步的改良，以擾動項ε的變異數σ^2為標準，採用向後刪除的概念提出方法一及方法二，也將其改良後的方法透過張量積擴展到二維曲面的估計，以copula密度函數作為迴歸函數，與核迴歸中的局部線性迴歸的結果進行比較。 依模擬結果，方法一會因為σ的估計膨脹而篩選掉過多節點，方法二受σ的估計影響較小，估計效果較佳，也較為穩定。 在以copula密度函數作為迴歸函數的模擬實驗中，較不平滑的迴歸函數使用方法二來估計，估計效果較佳；較平滑的迴歸函數使用局部線性迴歸來估計為最佳，但如果在σ的估計上能更好，方法二的估計效果可能優於局部線性迴歸。

This thesis is based on the multi-resolution B-spline basis knots placement method proposed by Yuan[12] to further improve the selection of knots. Based on the variation of the disturbance term, Method 1 and Method 2,are proposed using the concept of backward deletion. The improved method is also extended to the estimation of the two-dimensional surface. through the tensor product. Simulation studies have been carried out to compare the performance of Methods 1 and 2, and local linear regression. According to the results of simulation studies, Method 1 tends to filter out too many knots because of the large estimation error of σ,and Method 2 is less affected by the estimation of σ. The estimation based on Method 2 is more accurate and stable. In the studies where Methods 1 and 2, and local linear regression are compared, Method 2 outperforms local linear regression when the regression function is less smooth. When the regression function is smooth, local linear regression performs better than Method 2. However,if the estimation of σ can be better, the estimation accuracy of Method 2 may be better than local linear regression.

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