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Small Area Estimation of Income Under Spatial SAR Model

100%

Kubacki J., Jędrzejczak A.

Statistics in Transition new series

2016

vol. 17

issue 3

365-390

The paper presents the method of hierarchical Bayes (HB) estimation under small area models with spatially correlated random effects and a spatial structure implied by the Simultaneous Autoregressive (SAR) process. The idea was to improve the spatial EBLUP by incorporating the HB approach into the estimation algorithm. The computation procedure applied in the paper uses the concept of sampling from a posterior distribution under generalized linear mixed models implemented in WinBUGS software and adapts the idea of parameter estimation for small areas by means of the HB method in the case of known model hyperparameters. The illustration of the approach mentioned above was based on a real-world example concerning household income data. The precision of the direct estimators was determined using own three-stage procedure which employs Balanced Repeated Replication, bootstrap and Generalized Variance Function. Additional simulations were conducted to show the influence of the spatial autoregression coefficient on the estimation error reduction. The computations performed by ‘sae’ package for R project and a special procedure for WinBUGS reveal that the method provides reliable estimates of small area means. For high spatial correlation between domains, noticeable MSE reduction was observed, which seems more evident for HB-SAR method as compared with the traditional spatial EBLUP. In our opinion, the Gibbs sampler, revealing the simultaneous nature of processes, especially for random effects, can be a good starting point for the simulations based on stochastic SAR processes.

Application of bayesian estimation methods for small domains in the Polish Labor Force Survey

88%

Kubacki J., Centre for Statistical Surveys Realisation S. O. i. Ł.

Acta Universitatis Lodziensis. Folia Oeconomica

2008

vol. 216

The author presents a synthetic overview of recent efforts related to the small area estimation methods applied to the Polish Labor Force Survey (PLFS). The review concerns methodology and results obtained by Central Statistical Office connected with PLFS and National Census and some results obtained by the author of this paper. In the paper author discusses various methods of estimation together with evaluation of quality of such estimation. In particular the relationship between quality of Bayes estimates type and quality of a priori estimates and also type of applied method of estimation is presented.

Referat przedstawia syntetyczny przegląd przeprowadzonych ostatnio badań, dotyczących zastosowania metod statystyki małych obszarów, z użyciem wyników z Badania Aktywności Ekonomicznej Ludności. Przegląd dotyczy zagadnień metodologicznych oraz wyników otrzymanych przez Główny Urząd Statystyczny, związanych z BAEL oraz Spisem Powszechnym 2002, jak również wynikami otrzymanymi przez autora niniejszego referatu. W referacie dyskutowane są różne metody estymacji, łącznie z szacunkami ich jakości. W szczególności przedstawione została zależność jakości danych szacowanych z użyciem metod bayesowskich od jakości szacunków a priori oraz rodzaju zastosowanej metody estymacji.

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1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Statistics in Transition new series

1 2016

1 2008

2 Kubacki J.

1 Centre for Statistical Surveys Realisation S. O. i. Ł.

1 Jędrzejczak A.

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Small Area Estimation of Income Under Spatial SAR Model

Application of bayesian estimation methods for small domains in the Polish Labor Force Survey