Estimation of variance of random effect in small area model with Spatial Empirical Best Linear Unbiased Prediction (SEBLUP)

Survey sampling is one of the sampling methods of an object to provide information estimation of population parameters that became the focus of research. One of the methods that used to estimate population parameters is direct estimation method. However, when the direct estimation is used it will cause a large standard error. To handle that problem in small area we add information about the same parameters in other small areas which has similar character, or the value of the variables that are related to the variables being observed, this method is known as the small area estimation (SAE). In this mini thesis, small area method that we use consider spatial correlation between area, spatial Empirical Best Linear Unbiased Prediction (EBLUP). The estimator of spatial EBLUP depends on the variance component and spatial correlation, but in practice they are unknown. Therefore, to get the spatial EBLUP estimator it is necessary to first estimate the variance of random effect and correlations between area. In this mini thesis we use maximum likelihood method and scoring algorithm to estimate the variance of random effect and correlations between area.