Empirical Best Linear Unbiased Prediction for Out of Sample Areas

Abstract

Models for small area estimation based on a random effects specification typically assume population units in different areas are uncorrelated. However, they can be extended to account for the correlation between areas by assuming that area random effects are spatially correlated. In this paper we suggest a simple variance-covariance structure for such a spatial correlation structure within the context of a linear model for the population characteristic of interest, and derive estimates of parameters and components of variance using maximum likelihood and restricted maximum likelihood methods. This allows empirical best linear unbiased predictions for area totals to be computed for areas in sample as well as those that are not in sample. An expression for the mean cross-product error (MCPE) matrix of these predicted small area totals is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation.

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