Small area estimation: An application of a flexible fay-herriot method

The importance of small area estimation in survey sampling is increasing, due to the growing demand for reliable small area estimation from both public and private sectors. In this paper, we address the important issue of using statistical modeling techniques to compute more reliable small area estimates. The main aim is to assess the use of a flexible methodology for small area estimation. We formulate a new flexible small area model by incorporating a tuning (index) parameter into the standard area-level (Fay-Herriot) model. We achieve this using a combination of two methods namely, empirical Bayes (EB) approach and hierarchical Bayes (HB) approach. Our results suggest that the proposed model can be seen as advancement over the standard Fay-Herriot model. The novelty here isthat we have developed a flexible way to handle random effects in small area estimation. The Implementation of the proposed model is only mildly more difficult than the Fay-Herriot model. We have obtained results for both EB approach and the HB approach. Compared with the corresponding HB procedure, the EB approach saves a tremendous computing time and is very simple to implement.Key words: Area-level, empirical Bayes, Fay-Herriot model, hierarchical Bayes, small are

Bootstrap for estimating the mean squared error of the spatial EBLUP

This work assumes that the small area quantities of interest follow a Fay-Herriot model with spatially correlated random area effects. Under this model, parametric and nonparametric bootstrap procedures are proposed for estimating the mean squared error of the EBLUP (Empirical Best Linear Unbiased Predictor). A simulation study compares the bootstrap estimates with an asymptotic analytical approximation and studies the robustness to non-normality. Finally, two applications with real data are described

Bootstrap for estimating the mean squared error of the spatial EBLUP

This work assumes that the small area quantities of interest follow a Fay-Herriot model with spatially correlated random area effects. Under this model, parametric and nonparametric bootstrap procedures are proposed for estimating the mean squared error of the EBLUP (Empirical Best Linear Unbiased Predictor). A simulation study compares the bootstrap estimates with an asymptotic analytical approximation and studies the robustness to non-normality. Finally, two applications with real data are described.

Analytic and bootstrap approximations of prediction errors under a multivariate fay-herriot model

A Multivariate Fay-Herriot model is used to aid the prediction of small area parameters of dependent variables with sample data aggregated to area level. The empirical best linear unbiased predictor of the parameter vector is used, and an approximation of the elements of the mean cross product error matrix is obtained by an extension of the results of Prasad and Rao (1990) to the multiparameter case. Three different bootstrap approximations of those elements are introduced, and a simulation study is developed in order to compare the efficiency of all presented approximations, including a comparison under lack of normality. Further, the number of replications needed for the bootstrap procedures to get stabilized are studied