Statistical properties of the mean square prediction error of provincial EBLUP [Empirical B est Linear Unbiased Prediction] estimates of poverty incidence in the Philippines

This study used the generalized variance function (GVF) method to construct a model to estimate the sampling error variances in small area estimation using the Empirical Best Linear Unbiased Prediction (EB LUP) technique. The Prasad-Rao MSPE estimator is modified by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimators and four jackknife-based estimators is evaluated through a simulation study. Different methods of estimating the model variance is likewise investigated in the simulation. Results have shown that using GVF estimates of the sampling error variances leads to substantial gain in efficiency of the modified Prasad-Rao MSPE estimator over the commonly used Prasad-Rao MSPE estimator to as much as 876%, on the average. This implies that the GVF approach has been proven to be successful in resolving the issue on unknown or sometimes nonexistent mean square error or sometimes nonexistent mean square error of direct estimates of small area parameters. The modified Prasad-Rao MSPE estimator performs quite well on the simulation study and may be used to measure the reliability of EBLUP estimates when the sampling error variances are estimated using a GVF model. The modified Prasad-Rao estimator performs best when the model variance is estimated by maximum likelihood or restricted maximum likelihood method. The percentage of provinces having estimates of poverty incidence with coefficient of variation at most 10% has increased from 45.45% using direct estimation to as much as 68.33% using EBLUP approach with the modified Prasad-Rao MSPE estimator. The composition of the ten poorest provinces based on the direct estimates and the EBLUP estimates of poverty incidence are not much different particularly on the first to the seventh rank. The provinces occupying the eighth to tenth rank vary between direct and EBLUP estimates. Based on both direct and EBLUP estimates of poverty incidence, Sulu is the poorest province while the least poor province is Batanes. It is recommended that the GVF method be used to estimate sampling error variance together with the modified Prasad-Rao MSPE estimator in generating EBLUP estimates of poverty incidence at the provincial or even municipal level. Likewise, it is recommended that these methods should be applied to small area estimation problems involving rates or proportions whose average is close to 0.5 since the normal approximation to the binomial distribution applies in these cases and this warrants the use of maximum likelihood and restricted likelihood methods in estimating the model variance.