On small-area estimation under two-fold nested error regression models

Estimation of small-area means under a two-fold nested error regression models is considered. The best linear unbiased estimator (BLUP) of a small-area mean is obtained explicitly under this model. The unknown variance components involved in the BLUP estimator are then replaced by estimators obtained from a simple transformation method. An estimator of the MSE of the resulting empirical BLUP (EBLUP) estimator, correct to second-order terms, is also obtained, assuming the number of small areas to be large. Results of a simulation study on the relative bias of the MSE estimator are reported. (C) 1999 Elsevier Science B.V. All rights reserved.