Small Area Estimation : The Empirical Best Predictor Based on a Log Transformed Model with Spatially Correlated Random Effects

Dian Handayani, Henk Folmer, Asep Saefuddin and Anang Kurnia

 

Abstract

 Standard Small Area Estimation (SAE) based on a linear mixed model assumes that the variable of interest follows a normal distribution and has a linear relationship with some auxiliary variables. In practice, however, for example in socio-economic and health, the variable of interest is typically highly skewed. Besides normality, standard SAE model also assumes independence between small areas, whereas in practice, there is often spatial dependence in that the variable of interest in one area is related to their counterparts in neighboring areas.

Karlberg (2000a) studied the estimation of population total for highly skewed data and developed a bias correction factor to derive an approximately unbiased predictor. The bias correction is based on the assumption that the logarithm transformation of the variable of interest follows normal distribution. Kurnia and Chambers (2011) adopted the bias correction’s Karlberg for highly skewed data to the estimator of small area mean. However, Karlberg nor Kurnia and Chambers considered spatial dependence between small areas.

In this paper, we propose the empirical best predictor of the small area mean for highly skewed data in the presence of spatial dependence between small areas. The estimator of mean squared error of the predictor is obtained by Taylor linearization. The relative performance of the proposed predictor is evaluated through a Monte Carlo simulation.

Keywords : small area estimation, skewed data, spatial dependence, spatial empirical best predictor

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Dian Handayani: Department of Mathematics Jakarta State University – Indonesia, Faculty of Spatial Sciences University of Groningen – The Netherlands, email : dian99163@yahoo.com

Henk Folmer: Faculty of Spatial Sciences University of Groningen – The Netherlands, College of Economics and Management Northwest Agriculture and Forestry University Yangling – China, email : h.folmer@rug.nl

Asep Saefuddin : Department of Statistics  Bogor Agricultural University – Indonesia, email : asaefuddin@gmail.com

Anang Kurnia : Department of Statistics Bogor Agricultural University – Indonesia, email : anangk@apps.ipb.ac.id

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