Estimating a Bounded Normal Mean Relative to Squared Error Loss Function

Let x1,..., xn be a random sample from a normal distribution with unknown mean θ and known variance σ^2 the usual estimator of the mean, i.e., sample mean xbar, is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, θ is known in advance to lie in an interval, say [ -m,m] for some m>0 in this case, the maximum likelihood estimator changes and dominates xbar 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 xbar and the maximum likelihood estimator is not recommended when some information are accessible about the finite bounds on [ -m,m] in advance. based on the values taken by θ in [ -m,m] , the appropriate estimator is suggested.