No abstract

We propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.Keywords: Empirical best estimator; Parametric bootstrap; Poverty mapping; Small area estimation. AbstractWe propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.

We describe the R package sae for small area estimation. This package can be used to obtain model-based estimates for small areas based on a variety of models at the area and unit levels, along with basic direct and indirect estimates. Mean squared errors are estimated by analytical approximations in simple models and applying bootstrap procedures in more complex models. We describe the package functions and show how to use them through examples. The R package at a glance The R package sae implements small area estimation methods under the following area-level models: • Fay-Herriot model (including common fitting methods); • extended Fay-Herriot model that accounts for spatial correlation; • extended Fay-Herriot model allowing for spatio-temporal correlation. The package also includes small area estimation methods based on the basic unit level model called the nested-error linear regression model. The available estimation methods under this model are: • Empirical best linear unbiased predictors (EBLUPs) of area means under the nested-error linear regression model for the target variable. • Empirical Best/Bayes (EB) estimates of general nonlinear area parameters under the nested-error linear regression model for Box-Cox or power transformations of the target variable. Methods for estimation of the corresponding uncertainty measures of the small area estimators obtained from the above models are also included. Additionally, the package includes the following basic direct and indirect estimators • Direct Horvitz-Thompson estimators of small area means under general sampling designs; • Post-stratified synthetic estimator; • Composite estimator. This paper describes the above model-based small area estimation techniques and illustrates the use of the corresponding functions through suitable examples. For a description of the direct and basic indirect estimators included in the package and a detailed description of all implemented methodology, see http://CRAN.R-project.org/package=sae.

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163-171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad-Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors.

No abstract