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系統識別號 U0026-0812200911550631
論文名稱(中文) 相關常態母體中最大均數之最優信賴區間
論文名稱(英文) Optimal Confidence Interval for the Largest Mean of Correlated Normal Populations
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 94
學期 2
出版年 95
研究生(中文) 李秀玲
研究生(英文) Hsiu-Ling Li
學號 r2693402
學位類別 碩士
語文別 英文
論文頁數 130頁
口試委員 口試委員-吳宗正
指導教授-陳占平
指導教授-溫敏杰
中文關鍵字 共同基金  臨界值  最適均數組合配置  最優信賴區間 
英文關鍵字 Mutual Funds.  Critical Values  Least Favorable Configuration  Optimal Confidence Interval 
學科別分類
中文摘要   在多個相關的常態母體中,使用單一抽樣方法求得最大均數或最小均數之最優信賴區間。假設資料具有共同且未知的變異數,以及具有共同已知且為非負的的相關係數,依據最適均數組合配置,在任意信賴常數下,首先求得信賴區間涵蓋機率下限,然後調整信賴常數,求得最大化的涵蓋機率並達到預定高水準(例如95%信賴水準)。在相關的常態母體中,最大(最小)均數之最優信賴區間,所必須的臨界值已經製成統計表格於附錄中。最後,將本信賴區間應用於共同基金報酬率的估計上。


英文摘要   A single-sample sampling procedure for obtaining an optimal confidence interval for the largest or smallest mean of several correlated normal populations is proposed. It is assumed that the common variance is unknown and the common correlation coefficient is a given non-negative value. This optimal confidence interval is obtained by maximizing the coverage probability with the expected confidence width being fixed at a least favorable configuration of means.Tables of the critical values are made to implement the optimal confidence interval
for the largest (or smallest) mean of correlated normal populations. Finally, we apply this optimal confidence interval procedure to obtain an optimal confidence interval for the largest return of diversified mutual funds in the United States.


論文目次 1 Introduction 1
2 literature Review 3
2.1 Optimal confidence Interval for the Largest Normal Mean with Unknown
Variance...............................................................3
2.2 Optimal Confidence Interval for the Largest Mean in Repeated Measurements
Design.................................................................4
3 Methodology 7
3.1 Optimal Confidence Interval............................................7
3.2 Optimal Confidence and Numerical Solution.............................11
3.3 Testing for the Equal Correlation Structure...........................14
3.4 Example...............................................................15
4 Conclusion and Discussion 19
References 21
Appendix A 22
Appendix B 25
Appendix C 66
參考文獻 Chen, H. J., Chen, S. Y., 1999. A nearly optimal confidence interval for the
largest normal mean. Communications in Statistics: Simulation and
Computation 28(10), 131-146.
Chen, H. J., Chen, S. Y., 2004. Optimal confidence interval for the largest
normal mean with unknown variance. Computational Statistics and Data
Analysis 47, 845-866.
Chen, H. J., Tsai, P. J., 1980. Optimal confidence interval for the largest
mean in repeated measurements design. Biometrika 67(1), 119-126.
Dudewicz, E. J., Tong, Y. L., 1971. Optimal confidence interval for the
largest location parameter. Statistical Decision Theory and Related Topics.
(S.S. Gupta and J. Yackel, Eds.) New York: Academic Press, Inc., 363-375.
Dudewicz, E. J., 1972. Two-sided confidence intervals for ranked means.
Journal of the American Statistical Association 67, 462-464.
Johnson, R. A., Wichern, D. W., 2002. Applied multivariate statistical
analysis (4th Ed.), Upper Saddle River, New Jersey: Prentice Hall.
Lawley, D. N., 1963. On testing a set of correlation coefficients for
equality. Annals of Mathematical Statistics 34, 149-151.
Saxena, K. M. L., Tong, Y. L., 1969. Interval estimation of the largest mean
of k normal populations with known variance. Journal of the American
Statistical Association 64, 269-299.
Saxena, K. M. L., 1976. A single-sample procedure for the estimation of the
largest mean. Journal of the American Statistical Association 71, 147-148.
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