題　目：Improved Estimators for the Common Mean and Ordered Means of Two Normal Distributions with Ordered Variances 主講人：張元宗教授 (日本目白大學) 時　間：101年6月22日(星期五)上午10:40-11:30 地　點：交大綜合一館427室 Abstract We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959). Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators. However, in terms of estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is discussed. --

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