Small Area Estimation Under a Restriction

There are many situations in which it is desirable to derive reliable estimators for small geographical areas or small subpopulations, from existing survey data. The basic random e ects model and corresponding small area predictors for small area estimation is introduced. There are also many situations in which it is necessary to have the total of the small area predictors equal to the total of the direct survey estimates for many small areas. This motivates the small area estimation under a restriction, which forces the sum of the small area predictors equal to certain benchmark. Several small area predictors under a restriction are reviewed. A criterion that uni es the derivation of these restricted predictors is proposed. The predictor that is the unique best linear unbiased estimator under the criterion is derived. The derivation of the mean square error (MSE) of the restricted predictiors is discussed. Simulations are used to demonstrate that imposing a restriction can reduce the bias compare to that of the small area predictors without restriction.