本論文在B-spline的背景下進行密度估計，藉由類似帶寬選擇(bandwidth selection)的概念並提出一種挑選節點位置的準則，以估計出較平滑的機率密度函數。節點選取之準則主要透過「抽樣的留一最小平方交叉驗證」(sample leave-one-out least square cross validation) 挑選兩個調節參數並進行估計。通過本文分析不同模擬資料下的結果顯示，此挑選節點位置的準則在估計機率密度函數部分表現良好，因為平均下來的「積分均方誤差」(Integrated Squared Error)數值較小。

In this thesis, the problem of density estimation based on spline approximation is considered. A procedure for determining knot positions is proposed. The procedure involve two tunning parameters which are determined using sample leave-one-out cross validation. The simulation results indicate that the knot selection procedure performs well since the averages of integrated squared errors are small.

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