Estimation of parameters in the populations with the tree order constraint

Consider the problem of estimating the tree order meansμ۰ ≤μ۱ for all i = ۱, … , k from independent normal random variables. The restricted maximum likelihood estimator (RMLE) for the control group mean􀟤􀬴diverges to−∞and fails disastrously, in terms of mean squared error, especially when 􀝇 is large. Recently, Betcher and Peddada (۲۰۰۹) found some new estimators that stochastically dominate the unrestricted maximum likelihood estimator of control group mean􀟤􀬴which satisfied in sufficient conditions described in their paper. Consequently, we strengthen the previously known results regarding for structure of new control group estimator which dominates the unrestricted maximum likelihood estimator, uniformly, and does not failed in some of the situations where RMLE and two aforementioned estimators failed. Our simulation study suggests that the proposed estimator competes well with the existing estimators, especially when k is large. The gains of proposed estimator in terms of MSE with respect to other estimators can be substantial.