In this paper a geographical weighted pseudo empirical best linear unbiased predictor (GWEBLUP) for small area averages is proposed, and two approaches for estimating its mean squared error (MSE), a conditional approach and an unconditional one, are developed. The popular empirical best linear unbiased predictor (EBLUP) under the linear mixed model and its associated MSE estimator are obtained ...

Longitudinal surveys are very common in sampling over interval of times to estimate the aggregate level of population means at given point of time. In the present paper, the estimation methods have been developed for small area in longitudinal surveys using small area estimation (SAE) techniques. Direct, synthetic and composite estimators have been proposed to estimate the population mean of sm...

There are many situations in which it is desirable to derive reliable estimators for small geographical areas or small subpopulations, from existing survey data. The basic random e ects model and corresponding small area predictors for small area estimation is introduced. There are also many situations in which it is necessary to have the total of the small area predictors equal to the total of...

The problem of small area estimation (SAE) is how to produce reliable estimates of characteristics of interest such as means, counts, quantiles, etc., for areas or domains for which only small samples or no samples are available, and how to assess their precision. The purpose of this paper is to review and discuss some of the new important developments in small area estimation methods. Rao [Sma...

Calibrated weighting methods for estimation of survey population characteristics are widely used. At the same time, model-based prediction methods for estimation of small area or domain characteristics are becoming increasingly popular. This paper explores weighting methods based on the mixed models that underpin small area estimates to see whether they can deliver equivalent small area estimat...

Small area estimators are often based on linear mixed models under the assumption that relationships among variables are stationary across the area of interest (Fay–Herriot models). This hypothesis is patently violated when the population is divided into heterogeneous latent subgroups. In this paperwe propose a local Fay–Herriotmodel assisted by a SimulatedAnnealing algorithm to identify the la...

Survey data often contain measurements for variables that are semicontinuous in nature, i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linear mixed models can be inefficient for such variables. We discuss SAE techniques for se...

We derive a class of composite estimators of small-area quantities that exploit spatial (distance-related) similarity. They are based on a distribution-free model for the areas, but the estimators are aimed to have optimal design-based properties. Composition is applied also to estimating some of the global parameters on which the small-area estimators depend. We show that the commonly adopted ...