On small area estimation under a sub-area level model

We propose an extension of the well-known Fay and Herriot (1979) area level model to sub-area level. Not only this model may be used to estimate small area means by borrowing strength from related areas, but also by borrowing strength from sub-areas to obtain more efficient sub-area estimators. Model-based empirical best linear unbiased prediction (EBLUP) estimators are obtained from the BLUP estimators by replacing the model parameters by suitable estimators, using an iterative method based on weighted residual sum of squares. Second order approximations to the mean squared error (MSE) of the EBLUP estimators are obtained and then used to drive MSE estimators unbiased to second order. Results of simulation studies on the performance of the proposed estimators are also provided.