University of TehranJournal of Sciences, Islamic Republic of Iran1016-110422320110901Estimating a Bounded Normal Mean Relative
to Squared Error Loss FunctionEstimating a Bounded Normal Mean Relative
to Squared Error Loss Function26727623589ENA.KarimnezhadAllameh Tabatabaâ€™i
UniversityJournal Article19700101Let be a random sample from a normal distribution with unknown mean and known variance The usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. In many practical situations, is known in advance to lie in an interval, say for some In this case, the maximum likelihood estimator changes and dominates but it is no longer admissible. Minimax and some other estimators for this problem have been studied by some researchers. In this paper, a new estimator is proposed and the risk function of it is compared with some other competitors. According to our findings, the use of and the maximum likelihood estimator is not recommended when some information are accessible about the finite bounds on in advance. Based on the values taken by in , the appropriate estimator is suggested.https://jsciences.ut.ac.ir/article_23589_c00c9b7bdf289e4d84aa381dfa227d26.pdf