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博碩士論文 etd-0723108-160542 詳細資訊
Title page for etd-0723108-160542
論文名稱
Title
小樣本下拔靴法對變異數一致性檢定之檢定力分析
Power Analysis of Bootstrap Methods for Testing Homogeneity of Variances with Small Sample
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
24
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2008-06-19
繳交日期
Date of Submission
2008-07-23
關鍵字
Keywords
Levene 檢定、拔靴法、Bartlett 檢定
Levene's test, Bartlett's test, Bootstrap method
統計
Statistics
本論文已被瀏覽 5726 次,被下載 1515
The thesis/dissertation has been browsed 5726 times, has been downloaded 1515 times.
中文摘要
以往已有許多典型的變異數一致性檢定被廣泛地研究與討論著。然而若在小樣本的情況底下,這些一致性檢定之統計量卻無法擁有好的表現。在本文中,我們將探討運用拔靴法在小樣本下執行變異數一致性檢定的流程。對於檢定之靈活性與穩健性是我們提出以重抽方式進行檢定流程的重要特徵。在此我們也將比對所有檢定程序之型一誤差與檢定力的表現。
Abstract
Several classical tests are investigated for testing the homogeneity of variances. However, in case of homoscedasticity statistics do not perform well with small sample size. In this article we discuss the use of bootstrap technique for the problem of testing equality of variances with small samples. Two important features of the proposed resampling method are their flexibility and robustness. Both α levels and power of our new proposed procedure is compared with the other classical methods discussed here.
目次 Table of Contents
Abstract
1 Introduction
2 Preliminaries
2.1 Bartlett’s test
2.2 Levene’s test
2.3 Bootstrap method
2.3.1 Smooth Bootstrap
3 The test procedures of bootstrap method
4 Simulated critical values of binomial procedures with small sample
5 Power Comparisons
6 Real Example
7 Conclusions
Appendix
References
參考文獻 References
Bartlett, M. S. (1937), “Properties of Sufficiency and Statistical Tests,” Proceedings of the Royal Statistical Society, Ser. A, 160, 268-282.
Boos, D. D. and Brownie C. (1989), “Bootstrap Methods for Testing Homogeneity of Variances,” Technometrics, 31, 69-82.
Brown, M. B. and Forsythe A. B. (1974), “Robust Tests for the Equality of Variances,” Journal of the American Statistical Association, 69, 364-367.
Efron, B. (1979), “Bootstrap Methods: Another Look at the Jackknife,” The Annals of Statistics, 7, 1-26.
Hesterberg, T. C. (1999), “Smoothed Bootstrap and Jackboot Sampling,” Research Department 87, MathSoft, Inc., 1700 Westlake Ave. N., Suite 500, Seattle, WA 98109.
Levene, H. (1960), “Robust Tests for Equality of Variance,” In Contributions to Probability and Statistics, ed. I. Olkin, Palo Alto, CA: Stanford University Press, 278-292.
Shrivas, K. and Wu, H. F. (2007), “A Simple and Rapid Quantitative Method by Direct Coupling Drop-to-Drop Solvent Microextraction (DDSME) with Gas Chromatography/Mass Spectrometry to Determine Caffeine in One Drop of Beverages and Foods,” Journal of Chromatography, Ser. A, 1170, 9-14.
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