Open Conference Systems, ITACOSM 2019 - Survey and Data Science

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On synthetic median estimator in small area estimation
Tomasz Stachurski

Building: Learning Center Morgagni
Room: Aula Magna 327
Date: 2019-06-05 04:20 PM – 06:00 PM
Last modified: 2019-05-23

Abstract


In socio-economic studies, researchers are interested in characterizing a distribution of studied variable. The parameter of practical interest is a population median. The paper is devoted to the problem of the small area estimation of the median. In the design-based approach there are two main kinds of estimators: direct and indirect. In small area, direct estimators have limited applications, due to the fact that in the case of small domain sample sizes, such estimators have huge values of the variance. On the contrary, indirect estimators due to use of some auxiliary information, are much more accurate and what is more, indirect estimators can be used even though, the domain sample size equals zero. The main aim of this paper is to analyse properties of synthetic ratio median estimator. One the one hand, indirect estimators are more accurate than direct estimators, but on the other hand using synthetic estimators is linked to the assumption of similarity of the domain of interest to the population, which is not always fulfilled. In the paper there are presented derivations of its bias and mean square error. They are compared to the bias and MSE of synthetic ratio mean estimator. In the simulation study, based on real data, there are computed values of components of both the bias and MSE of synthetic estimator.


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