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題名 | 核密度函數估計時變動帶寬選取法=Variable Bandwidth Selection for Kernel Density Estimation |
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作者 | 吳鐵肩; 陳俞吟; | 書刊名 | 中國統計學報 |
卷期 | 41:1 2003.03[民92.03] |
頁次 | 頁81-96 |
分類號 | 314.5 |
關鍵詞 | 核估計; 特徵函數; 連結方法; 群集分析; 變動帶寬; 整體平滑參數; Characteristic function; Cluster analysis; Global smoothing parameter; Kernel density estimator; Linkage method; Variable bandwidth; |
語文 | 中文(Chinese) |
中文摘要 | 根據來自未知密度函數f的n個隨機樣本,我們研究f的核估計量的變動帶寬 (variable b andwidth) 選取法。針對此問題,一般戰略是將變動帶寬表示成局部帶寬因子 (local bandwidth factor) 和整體平滑參數 (global smoothing parameter) 的乘積。我們提出兩種選取局部帶寬因子的方法,這兩種方法都是直覺上可行的。其中一種方法是根據資料的群集分析(cluster analysis) ,而另一種方法是根據資料的誤差分析 (deviation analysis)。至於我們所提出的選取整體平滑參數 的方法是由Chiu (1991a,1992) 的頻率域 (frequency domain) 方法衍生而來。此外,我們做了大規模的模擬研究以比較我們變動帶寬選取法和Abramson (1982) 的選取法。模擬結果顯示群集方法有較最好的整體表現。 |
英文摘要 | Based on a random sample of size n from an unknown density f, the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth as the product of a local bandwidth factor and a global smoothing parameter. Two methods of selecting the local bandwidth factor are proposed. Both methods are direct and intuitively appealing. One method is based on the cluster analysis of the data, and the other method is based on the deviation analysis of the data. An adaptation of the frequency domain approach of Chiu (1991a, 1992) is used to select the global smoothing parameter. Extensive simulation studies have been done to compare the performance of our variable bandwidth selectors with the selector of Abramson (1982), and the superior performance of the cluster method at practical sample sizes is clearly demonstrated. |
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