The conference is organized by Maastricht University School of Business and Economics and Statistics Netherlands and will be held in Maastricht in the faculty building of Maastricht University School of Business and Economics on August 17-19, 2016
December 18-21 , 2014
IPB INTERNATIONAL CONVENTION CENTER
Department of Statistics
Bogor Agricultural University
Islamic Countries Society of Statistical Sciences
Anang Kurnia1), Dian Kusumaningrum1), Pika Silvianti1) and Dian Handayani2)
1) Department of Statistics, Bogor Agricultural University – Indonesia
2) Department of Mathematics, Jakarta State University – Indonesia
Many research on small area estimation (SAE) is typically based on a linear mixed model (LMM) assumptions. When the relationship between the interest and the auxiliary variables is not linear in the original scale, the SAE based on LMM could be inefficient. However, in practice, particularly in economic fields, the interest variable such as revenue or expenditure often does not follow normal distribution.
In this paper we will discuss the performance of SAE when the variable of interest does not follow normal distribution, but particularly it can be modeled by log-scaled transformation. Kurnia and Chambers (2011) used the bias correction proposed by Karlberg (2000) to produce the estimator of the small area mean for positively skewed data. However, the extreme outliers still affect the outcomes of the estimation. To overcome this matter, we used winsorization technique in linear mixed model fitting. The results indicated that Winsorization technique can be used as an alternative method to overcome outliers in SAE.
Keywords: winsorization, long tail distribution, small area estimation
Rahma Anisa, Anang Kurnia, and Indahwati
Department of Statistics, Bogor Agricultural University – Indonesia
Empirical Best Linear Unbiased Predictor (EBLUP) has been widely used to predict parameters in area with small or even zero sample size. The problem is when this model should be used to predict the parameters of non-sampled area. Ordinary EBLUP predicted the parameters using synthetic model which ignore the area random effects because lack of non-sampled area information. Thus, those prediction will be distorted based on a single line of the synthetic model. One of idea that developed in this paper is to modify the prediction model by adding cluster information by assuming that there are similiarities among particular areas. These information will be added into the model to modify the intercept of prediction model. Another approach is by adding random effects of auxiliary variable into the previous model in order to modify both intercept and slope of the prediction model. In this paper, simulation process is carried out to study the performance of the proposed models compared with ordinary EBLUP. All models evaluated based on the value of Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE). The result of simulation showed that the addition of cluster information can improve the ability of the model to predict on non-sampled areas.
Keywords: EBLUP, Clustering, Linear Mixed Models.
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
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
Dian Handayani: Department of Mathematics Jakarta State University – Indonesia, Faculty of Spatial Sciences University of Groningen – The Netherlands, email : email@example.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 : firstname.lastname@example.org
Asep Saefuddin : Department of Statistics Bogor Agricultural University – Indonesia, email : email@example.com
Anang Kurnia : Department of Statistics Bogor Agricultural University – Indonesia, email : firstname.lastname@example.org