Small Area Estimation of Sub-District’s Per Capita Expenditure through Area Effects Selection using LASSO Method

Abstract

Abstract This paper discusses a small area estimation (SAE) problem when the number of small areas is relatively small compared to size of the observations. This problem is known as a sparsity problem which can caused slow convergence in obtaining the parameter estimates. The sparsity problem on small area can be imposed by assigning zero for i-th area with adequate sample size, whereas it preserve the nonzero value for i-th small area. The sparsity of area specific effects vector brings heavy tails if the SAE method cannot properly handle this complexity of specific area effect characteristic. Thus, the aim of this study is to investigate the sparsity issue by developing small area estimation model using the LASSO method to shrinkage the parameter estimates and select the area specific effects properly. The simulation results showed that the LASSO method produced the smallest mean square error (MSE) while the precision of the prediction were not significantly different when compared to other methods. The LASSO method was also applied to estimate the mean of per capita expenditure of sub-district levels in Kepulauan Bangka Belitung Province and produced smaller MSE when compared to other methods.