A state space model in small area estimation

Abstract

There have been two main topics developed by statisticians in a survey, i.e. sampling techniques and estimation methods. The current issues in estimation methods relate to estimation of a particular domain having small size of samples or, in more extreme cases, there are no sample available for direct estimation (Rao, 2003). There is a growing demand for reliable small area statistics in order to asses or to put into policies and programs. Sample survey data provide effective reliable estimators of totals and means for large area and domains. But it is recognized that the usual direct survey estimator performing statistics for a small area, have unacceptably large standard errors, due to the circumtance of small sample size in the area. In fact, sample sizes in small areas are reduced, due to the circumtance that the overall sample size in a survey is usually determined to provide specific accuracy at a macro area level of aggregation, that is national territories, regions and so on. The most commonly used models for this case, usually in small area estimation, are based on generalized linear mixed models (GLMM). It is happened some time that some surveys are carried out periodically so that the estimation could be improved by incorporating both the area and time random effects. In this paper we propose a state space model which accounts for the two random effects and is based on two equation, namely transition equation and measurement equation.