An Empirical Best Prediction Method for Logarithmic Transformation Model in Small Area Estimation with Particular Application to Susenas Data

ANANG KURNIA

Department of Statistics IPB

Abstract

Currently statistician has given attention seriously to small area statistics. Fay and Herriot (1979) are the first researchers who developed small area estimation (SAE) which is based on linear mixed model. The model, known as Fay-Herriot model, has become a reference in the developing of further research on SAE.

The research focuses on developing robust SAE method to overcome large ratio variation between small areas and total variation. The developed method is also robust with respect to misspecification model, in a sense that the model fails to capture the correct trend.  There are some reasons why these topics are selected as a focus of this research. Firstly, based on some preliminary studies in an application of SAE methods using BPS‘ data, some improvements on precision of estimation has been shown but it was still unsatisfactory. Secondly, the fact that the pattern of social and economic data is difficult to fulfill linear assumption which is required in standard SAE method. The transformation on response variable, independent variable or both can be used to linearized the relationship.

The lognormal empirical best prediction (EBP) model which are suggested in this research give better results than standard SAE models in terms of the smallest relative root mean square error (RRMSE). However, the relative bias is still large enough (approximately 8 %).  On the other hand, the evaluation model using mean square prediction error (MSPE) is underestimated which was indicated by ignoring estimation effect on error variance  and bias of lognormal EBP. In general, the suggested model improves the efficiency of estimation.

In this research, the efforts to reduce the bias on mean estimation of model lognormal EBP are still not explored yet.  Further research on these will improve performance the suggested model, including the correction factor on estimation of non-sampled unit. Meanwhile, the MSPE could be decreased analytically by modeling the effect of variance estimation through Taylor expansion or resampling technique such as jackknife and bootstrap.

Keywords : small area estimation, logarithmic transformation, empirical best prediction

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