進階搜尋


 
系統識別號 U0026-0812200911174383
論文名稱(中文) 多維核密度函數估計時變異帶寬之選取法
論文名稱(英文) Multivariate Variable Bandwidth Selection for Kernel Density Estimation
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 92
學期 2
出版年 93
研究生(中文) 陳清福
研究生(英文) Ching-Fu Chen
學號 R2691103
學位類別 碩士
語文別 英文
論文頁數 30頁
口試委員 口試委員-任眉眉
指導教授-吳鐵肩
口試委員-李隆安
中文關鍵字 變動帶寬  特徵函數  集群分析  連結方法  整體平滑參數  核估計 
英文關鍵字 variable bandwidth.  kernel density estimator  global smoothing parameter  cluster analysis  Characteristic function 
學科別分類
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 的核密度估計量的變動帶寬選取法。針對此問題,一般戰略是將變動帶寬表示成局部帶寬因子和整體平滑參數的乘積。我們提出了根據集群分析所建立的方法。至於選取整體平滑參數的方法是由 Chiu( 1991a, 1992)的頻率域衍生而來。於是對於一維、二維,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) 及 Scott(1996) 的選取法。模擬結果顯示群集方法有很好的整體表現。


英文摘要   Based on a random sample of size n from an unknown density, the problem of adaptively selecting the bandwidth in kernel estimation is investigated. The common strategy is to express the variable bandwidth as the product of a local bandwidth factor and a global smoothing parameter. The method based on cluster analysis is proposed.
We select the global smoothing parameter by taking an adaptation of the frequency domain approach of Chiu (1991a, 1992).For d=1 and d=2, extensive simulation studies have been done to compare the performance of our variable bandwidth selectors with the selector of Abramson (1982) and Scott (1996). The simulation results verify that the proposed cluster method performs much better than the Abramson's method and Scott’s method.
論文目次 1 Introduction 1
1.1 The adaptive kernel density estimation …………………………………. 1
1.2 Background and Motivation …………………………………………….. 2
1.3 A brief Review of the Variable Bandwidth Selection …………………….3
1.4 Measures of discrepancy: the MISE criteria ……………………………...4

2 The variable bandwidth procedure 6
2.1 The choice of the amount of smoothing at a data point ………………….6
2.2 The cluster method of selecting the local bandwidth factor ……………..7
2.3 The choice of the global smoothing parameter …………………………..8

3 Simulation results and conclusion 12
參考文獻 Abramson, I. S. (1982). On bandwidth variation in kernel estimates - a square root law. The Annals of Statistics, 10, 1217-1223.

Brillinger, D. R. (1981). Time Series Data Analysis and Theory. Holt, Rinehart and Winston, New York.

Chiu, S. T. (1991a). Bandwidth selection for kernel density estimation. The Annals of Statistics , 19, 1883-1905.

Chiu, S. T. (1991b). The effect of discretization error on bandwidth selection for kernel density estimation. Biometrika, 78, 436-441.

Chiu, S. T. (1992). An automatic bandwidth selector for kernel density estimation. Biometrika, 79, 771-782.
Hall, P. (1990). On the bias of variable bandwdith kernel estimates. Biometrika, 77, 529-535.

Hall, P., Hu, T. C. and Marron, J. S. (1995). Improved variable window kernel estimates of probability densities. The Annals of Statistics , 23, 1-10.

Johnson, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis
3rd Ed.. New Jersey: Prentice Hall.

Jones, M. C. (1990). Variable kernel density estimates. Austral. J. Statist., 32, 361-371.

Jones, M. C., Mckay, I. J. and Hu, T. C. (1994). Variable location and scale kernel density estimation. Ann. Inst. Statist. Math. 46, 521-535.

Marron, J. S. and Wand, M. P. (1992). Exact mean integrated squared error. The Annals of Statistics, 20, 712-733.

Silverman, B. W. (1982). Density estimation for Statistics and Data Analysis. Champman and Hall, London.

Terrell, G. R. and Scott, D. W. (1992). Variable kernel density estimation. The Annals of Statistics, 20, 1236-1265.

Wand, M. P. and Jones, M. C. (1993). Comparison of smoothing Parameterizations in bivariate kernel density estimation. Journals of the American Statistical Association, 88, 520-528.
Wand, M. P. and Jones, M. C. (1995). Kernel smoothing. Champman and Hall,London.

Wu, T. -J. (1995). Adaptive root n estimates of integrated squared density derivative. The Annals of Statistics, 23, 1474-1495.

Wu, T. -J. (1997). Root n bandwidth selectors for kernel estimation of density derivatives. Journals of the American Statistical Association, 92, 536-547.

Wu, T. -J., Teng, Yu-Kai and Tsai, Min-Hsiao (2003). Root n bandwidths selectors in multivariate kernel density estimation. Probability Theory and Related Fields, 129, 537-558.

Wu, T. -J., Chen Yu-Yin, (2003). Variable bandwidth selection for kernel denstiy estimation. JCSA, 41, 81-96.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2004-08-30起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2004-08-30起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw