Comparison of some positive variance estimators for the Fay-Herriot small area model - ARCHIVED

The restricted maximum likelihood (REML) method is generally used to estimate the variance of the random area effect under the Fay-Herriot model (Fay and Herriot 1979) to obtain the empirical best linear unbiased (EBLUP) estimator of a small area mean. When the REML estimate is zero, the weight of the direct sample estimator is zero and the EBLUP becomes a synthetic estimator. This is not often desirable. As a solution to this problem, Li and Lahiri (2011) and Yoshimori and Lahiri (2014) developed adjusted maximum likelihood (ADM) consistent variance estimators which always yield positive variance estimates. Some of the ADM estimators always yield positive estimates but they have a large bias and this affects the estimation of the mean squared error (MSE) of the EBLUP. We propose to use a MIX variance estimator, defined as a combination of the REML and ADM methods. We show that it is unbiased up to the second order and it always yields a positive variance estimate. Furthermore, we propose an MSE estimator under the MIX method and show via a model-based simulation that in many situations, it performs better than other ‘Taylor linearization’ MSE estimators proposed recently.