Estimators of error covariance matrices for small area prediction

Prediction for the mixed model requires estimates of covariance matrices. There is often a direct estimate of the “within area” covariance matrix, and for survey samples this is an estimate of the sampling covariance matrix. The estimated covariance matrix may have large sampling variance, suggesting parametric modeling for the matrix. The model can play a role at various points in the construction of predictions for proportions for small areas. Simulations demonstrate that efficiency for predictions is improved by using a model for the covariance matrix in the estimator of mean parameters and in constructing the coefficients in the predictor.