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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.

IMPLEMENTACJA ODLEGŁOŚCI EKONOMICZNEJ DO MODELOWANIA KAPITALIZACJI WYBRANYCH GIEŁD

51%

Górna J., Górna K., Wleklińska D.

Metody Ilościowe w Badaniach Ekonomicznych

2014

vol. 15

issue 3

75-85

Celem artykułu jest analiza kapitalizacji wybranych giełd z perspektywy odległości ekonomicznej między nimi. Ze względu na charakter giełd – brak ścisłego związku z geograficzną lokalizacją, zaproponowana zostanie macierz oparta na odpowiednio zdefiniowanej odległości ekonomicznej. Takie podejście umożliwi sprawdzenie jak silnie na kształtowanie się wielkości kapitalizacji na jednej giełdzie wpływa wartość tego procesu na innych giełdach, które są podobne pod względem ekonomicznym. Ponadto sprawdzone zostanie, czy między wybranymi giełdami zachodzi zjawisko σ-konwergencji wielkości kapitalizacji.

The aim of the article is the analysis of capitalization of selected stocks from a perspective of economical distance. According to character of stocks – lack of connection to their spatial position, in investigated model the matrix founded on economical distance will be proposed. Thanks to that approach, it will be possible to investigate how powerful impact on stock capitalization has value of this process observed in the other stocks. Moreover, it will be investigated if among selected stocks σ-convergence phenomena of capitalization is observed.

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1 Metody Ilościowe w Badaniach Ekonomicznych

1 Statistics in Transition new series

1 Górna J.

1 Górna K.

1 Jędrzejczak A.

1 Kubacki J.

1 Wleklińska D.

1 2016

1 2014

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Small Area Estimation of Income Under Spatial SAR Model

IMPLEMENTACJA ODLEGŁOŚCI EKONOMICZNEJ DO MODELOWANIA KAPITALIZACJI WYBRANYCH GIEŁD