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相關文獻
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頁籤選單縮合
題名 | 轉換核密度函數估計法之邊界效應改善及偏差減小=Boundary Correction and Bias Reduction in Transformation Kernel Density Estimation |
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作者姓名(中文) | 洪萬吉; | 書刊名 | 大葉學報 |
卷期 | 13:1 2004.06[民93.06] |
頁次 | 頁17-22 |
分類號 | 440.11 |
關鍵詞 | 經驗分配轉換; 累積分配函數; 平滑參數; 偏差減小; 邊界效果; Empirical distribution transformation; Cumulative distribution function; Smoothing parameter; Bias reduction; Boundary effects; |
語文 | 中文(Chinese) |
中文摘要 | Ruppert與Cline [13] 提出轉換的核密度估計法,且使用它來估計未知密度函數。由於轉換的核密度估計量,在估計邊界區域時會造成所謂的邊界效果,本文提出利用Ruppert與Cline估計量與最小平方法結合之觀點,建立一個新的轉換的核密度估計量。所提之轉換的核密度估計量具有改善原Ruppert與Cline法之核估計量的缺點及不會產生估計值為負的優點。此外,所提之核估計量若結合在Ruppert與Cline [13] 之疊代法疊代j次,則偏差可達到O( ),hj為第j(31) 次疊代之帶寬,另本文也將提供所提估計量之收斂速率及建立其近似分配為常態。 |
英文摘要 | Ruppert and Cline [13] proposed the method of transformation-kernel density estimator, and used it to estimate the unknown density function. The transformation-kernel density estimator is known to have boundary effects. In this article, we propose a new transformation-kernel density estimator, which is a hybrid of the original Ruppert-Cline estimator and of the least squares method. The proposed method has the advantage of having positive resulting density estimator and it also improves upon the Ruppert-Cline method. Besides, when incorporated with the iterative method in Ruppert and Cline [13], the bias of the proposed estimator can achieve the order O( ), where hj is the bandwidth used in the j-th iteration. In this article, we also derive the convergence rate and establish the asymptotic normality for the proposed estimator. |
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