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頁籤選單縮合
題名 | A Simple Smooth Estimator in the Estimation of Density Derivatives=一個簡單的平滑估計量在密度導函數之估計 |
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作者 | 洪萬吉; Horng, W. J.; |
期刊 | 嶺東學報 |
出版日期 | 20010400 |
卷期 | 12 2001.04[民90.04] |
頁次 | 頁35-56 |
分類號 | 319.5 |
語文 | eng |
關鍵詞 | 最小二次式; 最小平方法; 核密度估計量; 邊界效果; 密度導函數; 整合均方差; 帶寬; 局部多項式擬合; 矩陣; 有界定義域; 向量; 偏差減小; Minimizing quadratic form; Least squares method; Kernel density estimator; Boundary effects; Density derivatives; Mean integrated square error; Bandwidth; Local polynomial fit; Matrix; Bounded domain; Vector; Bias reduction; |
中文摘要 | 在無母數密度估計裡,對密度導函數之估計是已被研究。當密度函數之定義域為 有界時,我們知道傳統的核估計量對密度導函數之估計也將遭遇到邊界效果的問題。為了 改善邊界效果與偏差減小,在本文中研究者依最小二次式的觀點來建立一個簡單且新的核 估計量。所提新的核估計量之簡潔的近似偏差,近似變異數和一些性質是將給與提供。除 此之外,研究者證明這所提估計量是沒有邊界效果及較傳統的核密度估計量為優;因此, 本文所提之估計量在邊界區域是不需要去修正它,且它的偏差之收斂速率是可達O(n□) ,對d=1,2,...,P≧1。 |
英文摘要 | In nonparametric density estimation, the estimation of density derivatives is already investigated. As the domain of density function is bounded, we known that the traditional estimator will also encounter the problem of the boundary effects for the estimation of density derivatives. In order to improve the boundary effects and bias reduction, one follow the idea of the minimizing quadratic form to construct a simple and new kernel estimator in this paper. The new proposed estimator, the compact form of the asymptotic bias, the asymptotic variance and some properties are given. Besides, the proposed estimator can be shown that it does not produce the boundary effects and be better than the tradition kernel density estimator; therefore, proposed estimator does not need to improve on the boundary regions, and the convergence rate of its bias is achieved O(n□) , for all d=1,2,..., P≧1. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。