TY - JOUR
ID - 32082
TI - Estimating a Bounded Normal Mean
Under the LINEX Loss Function
JO - Journal of Sciences, Islamic Republic of Iran
JA - JSCIENCES
LA - en
SN - 1016-1104
AU - Karimnezhad, A.
AD - Department of Statistics, Faculty of Mathematics, Statistics and Computer
Science, University of Tehran, Tehran, Islamic Republic of Iran
Y1 - 2013
PY - 2013
VL - 24
IS - 2
SP - 157
EP - 164
KW - Admissibility
KW - Bayes estimator
KW - LINEX loss function
KW - Maximum Likelihood Estimator
KW - Normal distribution
DO -
N2 - Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of minimax estimation of θ In this paper, by constructing a dominating class of estimators, we show that the maximum likelihood estimator is inadmissible. Then, as a competitor, the Bayes estimator associated with a uniform prior on the interval [−m,m] is proposed. Finally, considering risk performance as a comparison criterion, the estimators are compared and depending on the values taken by θ in the interval [−m,m], the appropriate estimator is suggested.
UR - https://jsciences.ut.ac.ir/article_32082.html
L1 - https://jsciences.ut.ac.ir/article_32082_f213688e182938621c667ee8a6906180.pdf
ER -