窗距的選取在核密度函數估計量扮演重要的角色，本文以平均積
分方差 (mean integrated square error, MISE) 與漸近平均積分方差(asymptotic mean integrated squared error, AMISE) 作為評估準則，探討六個機率分配，在不同樣本個數下的最佳窗距。直觀上，在資料密集的區域，給予較小的窗距，而資料稀疏的區域，給予較大的窗距，則核估計量將會較接近真實機率密度函數，故本文提出可變窗距之核密度函數估計量。可變窗距為局部窗距因子 (local bandwidth factor)與全域平滑參數 (global smoothing parameter) 的乘積，本文利用集群分析 (cluster analysis) 求得局部窗距因子，並藉由最小平方交叉驗證法 (least squared cross validation, LSCV) 得到全域平滑參數。最後利用電腦程式模擬對本文所提出的可變窗距之核密度函數估計量與Parzen (1962)、Abramson (1982) 的核估計量進行探討比較。

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