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Small area estimates based on the widely used area-level model proposed in Fay and Herriot (1979) assume that the area-level direct estimates are spatially uncorrelated. In many cases, however, this is not the case. Extensions of the Fay-Herriot model to allow for spatial correlation have been proposed, but all assume spatial stationarity; i.e., the parameters of the associated regression model for the small area characteristic of interest do not vary spatially. Instead, spatial effects are introduced by imposing a spatial correlation structure on the regression errors. In this paper, we propose an extension to the Fay-Herriot model that accounts for the presence of spatial nonstationarity, i.e., where the parameters of this regression model vary spatially. We refer to the predictor based on this extended model as the nonstationary empirical best linear unbiased predictor (NSEBLUP). We also develop two different estimators for the mean squared error of the NSEBLUP. The first estimator uses approximations similar to those in Opsomer, Claeskens, Ranalli, Kauermann, and Breidt (2008). The second estimator is based on the parametric bootstrapping approach of Gonzalez-Manteiga, Lombardia, Molina, Morales, and Santamaria (2008) and Molina, Salvati, and Pratesi (2009). Results from model-based and design-based simulation studies using spatially nonstationary data indicate that the NSEBLUP compares favorably with alternative area-level predictors that ignore this spatial nonstationarity. In addition, both proposed methods for estimating its mean squared error seem adequate. [ABSTRACT FROM AUTHOR]

In a special case of the general linear mixed model, one random component obeys a spatial autoregressive process and another a temporal autoregressive process. The population and any affiliations to subpopulations may change in time. The empirical best linear unbiased predictor is derived and may be used even if the sample size in the subpopulation is null in the period of interest. The mean squared error and its estimator are expressed. The accuracy of the predictor and the bias of the mean squared error estimator are addressed through simulations. [ABSTRACT FROM AUTHOR]

Statistical agencies are interested to report precise estimates of linear parameters from small areas. This goal can be achieved by using model-based inference. In this sense, random regression coefficient models provide a flexible way of modelling the relationship between the target and the auxiliary variables. Because of this, empirical best linear unbiased predictor (EBLUP) estimates based on these models are introduced. A closed-formula procedure to estimate the mean-squared error of the EBLUP estimators is also given and empirically studied. Results of several simulation studies are reported as well as an application to the estimation of household normalized net annual incomes in the Spanish Living Conditions Survey. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]