標題: | Generalized confidence intervals for the ratio of means of two normal populations |
作者: | Lee, JC Lin, SH 統計學研究所 資訊管理與財務金融系 註:原資管所+財金所 Institute of Statistics Department of Information Management and Finance |
關鍵字: | Fieller's theorem;generalized confidence interval;generalized p-values;generalized pivotal quantity;heteroscedasticity;pseudo Behrens-Fisher problem;ratio estimation |
公開日期: | 1-六月-2004 |
摘要: | Based on the generalized p-values and generalized confidence interval developed by Tsui and Weerahandi (J. Amer. Statist. Assoc. 84 (1989) 602), Weerahandi (J. Amer. Statist. Assoc. 88 (1993) 899), respectively, hypothesis testing and confidence intervals for the ratio of means of two normal populations are developed to solve Fieller's problems. We use two different procedures to find two potential generalized pivotal quantities. One procedure is to find the generalized pivotal quantity based directly on the ratio of means. The other is to treat the problem as a pseudo Behrens-Fisher problem through testing the two-sided hypothesis on 0, and then to construct the 1 - alpha generalized confidence interval as a counterpart of generalized p-values. Illustrative examples show that the two proposed methods arc numerically equivalent for large sample sizes. Furthermore, our simulation study shows that confidence intervals based on generalized p-values without the assumption of identical variance are more efficient than two other methods, especially in the situation in which the heteroscedasticity of the two populations is serious. (C) 2003 Elsevier B.V. All rights reserved. |
URI: | http://dx.doi.org/10.1016/S0378-3758(03)00141-1 http://hdl.handle.net/11536/26733 |
ISSN: | 0378-3758 |
DOI: | 10.1016/S0378-3758(03)00141-1 |
期刊: | JOURNAL OF STATISTICAL PLANNING AND INFERENCE |
Volume: | 123 |
Issue: | 1 |
起始頁: | 49 |
結束頁: | 60 |
顯示於類別: | 期刊論文 |