Improved direct estimators for small areas

Abstract

Unbiased direct estimators for small area estimation (SAE) are investigated and extended in this thesis.

Unbiased direct estimators for small area quantities are usually considered too variable to be of any practical use.  In this thesis we described a class of model based direct (MBD) estimators for small area quantities that appears to overcome this objection, in the sense that these estimators are comparable in efficiency to the indirect model-bases small area estimators (e.g. empirical best linear unbiased predictors, or EBLUPs) that are now widely used. There are many practical advantages associated with such MBD estimators, arising from the fact that they are computed as weighted linear combinations of the actual sample data from the small area of interest.  In this case the weights ‘borrow strength’ via a model that explicitly allows for small area effects. One particular advantage that we explore in this thesis is that estimation of mean squared error (MSE) is then straightforward, using well-known methods that are in common use for population level estimates.  Empirical results show that the MBD estimator represents a real alternative to the EBLUP, with the simple MSE estimator associated with the MBD estimator providing good coverage performance.  Further, our results indicate that the MBD estimator may be more robust than the EBLUP when the small area model is incorrectly specified.

We extended the MBD approach to multipurpose SAE.  Our results indicate these multipurpose weights are efficient across a range of variables, including variables that are ill-suited to EBLUP, e.g. variables that contain a significant proportion of zeros.  We also show that these multipurpose weights remain efficient across a wide range of variables, even variables that have not been used in the definition of the multipurpose weights.

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