Estimation of Ordered Means of Two Normal Distributions with Ordered Variances

作     者：Yuan-Tsung Chang Nobuo Shinozaki 

作者机构：Department of Social Information Faculty of Studies on Contemporary Society Mejiro University Tokyo 161-8539 Japan Department of Administration Engineering Faculty of Science and Technology Keio University Yokohama 223-8522 Japan 

出 版 物：《Journal of Mathematics and System Science》 (数学和系统科学（英文版）)

年 卷 期：2012年第2卷第1期

页      面：1-7页

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

主　　题：方差估计 正态分布 有序 估算 排列方式 均方误差 估计方差 小型企业 

摘      要：The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochastic domination and MSE (mean squared error). The authors show that in estimating the mean with larger variance, the usual estimator under order restriction on means can be improved upon. However, in estimating the mean with smaller variance, the usual estimator cant be improved upon even under MSE. The authors also discuss simultaneous estimation problem of two ordered means when unknown variances are ordered.