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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※ 編輯: cilar 來自: 140.113.114.180 (06/20 10:26)