Small Area Shrinkage Estimation

The need for small area estimates is increasingly felt in both the public and private sectors in order to formulate their strategic plans. It is now widely recognized that direct small area survey estimates are highly unreliable owing to large standard errors and coefficients of variation. The reason behind this is that a survey is usually designed to achieve a specified level of accuracy at a higher level of geography than that of small areas. Lack of additional resources makes it almost imperative to use the same data to produce small area estimates. For example, if a survey is designed to estimate per capita income for a state, the same survey data need to be used to produce similar estimates for counties, subcounties and census divisions within that state. Thus, by necessity, small area estimation needs explicit, or at least implicit, use of models to link these areas. Improved small area estimates are found by "borrowing strength" from similar neighboring areas.Comment: Published in at http://dx.doi.org/10.1214/11-STS374 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models

Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only $O(d^3n^{-3/2})$, where $d$ is the number of parameters and $n$ the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.Comment: Published in at http://dx.doi.org/10.1214/07-AOS512 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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