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| 研究生： |
莊耀程 Yao-Cheng Chuang |
|---|---|
| 論文名稱： |
標準常態核函數在密度函數之前二階導函數及曲率之核估計的應用 Application of Standard Gaussion Kernel Function on Kernel Estimators of the First Two Order Derivatives and Curvature of Probability Density Function |
| 指導教授： |
許玉生
Yu-Sheng Hsu |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 98 |
| 語文別： | 中文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 曲率之核估計 、導函數之核估計 |
| 外文關鍵詞： | Kernel Estimators of Derivatives, Kernel Estimators of Curvature |
| 相關次數： | 點閱：20 下載：0 |
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令f(x)表一機率密度函數，f''(x)及f''(x)分別表其第一、二階微
分，κ(x)表f(x)在x之曲率。f''(x)、f''(x)及k(x)提供f(x)之一些特性，為鑑別分布之重要參考。通常f(x)是未知的，所以f''(x)、f''(x)及κ(x)也未知，必需用樣本估計。本文討論f''(x)及f''(x)和κ(x)的核估計式。現有的文獻並未討論是否存在核函數使f''(x)及f''(x)之核估計式為漸近不偏，解決此問題為本文之首要目的，其結果將運用於估計κ(x)，並推出各估計式之中央極限定理。
In this paper, we find that the standard Guassian kernel function can be applied easily to construct the asymptotic unbiasedness of kernel estimators of the first two order derivatives of probability density function. we also find the central limit theorems for the kernel estimators mentioned above and the corresponding estimator of curvature.
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