TY - JOUR
T1 - Optimal confidence interval for the largest normal mean under heteroscedasticity
AU - Chen, Hubert J.
AU - Wen, Miin Jye
N1 - Funding Information:
This research was supported by the University of Georgia Research Foundation and National Science Council, NSC92-2119-M-006-007 and NSC93-2118-M-006-008, Taiwan, ROC, 2003–2005.
PY - 2006/11/15
Y1 - 2006/11/15
N2 - A two-stage sampling procedure for obtaining an optimal confidence interval for the largest or smallest mean of k independent normal populations is proposed, where the population variances are unknown and possibly unequal. The optimal confidence interval is obtained by maximizing the coverage probability with a fixed width at a least favorable configuration of means. Then, the sample sizes can be determined by this procedure. It has been shown that the optimal interval is globally optimal over all possible choices of symmetric and asymmetric intervals. In situations where the two-stage sampling procedure cannot be completely carried through, a one-stage sampling procedure can be implemented, and their relationship is discussed. A numerical example to demonstrate the use of these sampling procedures is given.
AB - A two-stage sampling procedure for obtaining an optimal confidence interval for the largest or smallest mean of k independent normal populations is proposed, where the population variances are unknown and possibly unequal. The optimal confidence interval is obtained by maximizing the coverage probability with a fixed width at a least favorable configuration of means. Then, the sample sizes can be determined by this procedure. It has been shown that the optimal interval is globally optimal over all possible choices of symmetric and asymmetric intervals. In situations where the two-stage sampling procedure cannot be completely carried through, a one-stage sampling procedure can be implemented, and their relationship is discussed. A numerical example to demonstrate the use of these sampling procedures is given.
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U2 - 10.1016/j.csda.2005.10.004
DO - 10.1016/j.csda.2005.10.004
M3 - Article
AN - SCOPUS:33750367971
SN - 0167-9473
VL - 51
SP - 982
EP - 1001
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 2
ER -