Kajian bias metode area-specific jackknife dan bias metode weighted jackknife dalam pendugaan area kecil untuk respon poisson dengan pendekatan bayes

Abstract

Small area estimation is a method to estimate parameters in a subpopulation with small sample size. The method is based on indirect estimation using the strength of the surrounding area and data sources outside the area to obtain statistic with edequate precision. Empirical Bayes (EB) method can be used to obtain estimates of small area parameters. In this paper the method was used to handle count data responses. The quality of an estimate can be measured by mean squared error (MSE). Wan (1999) proposed a weighted jackknife method for finding MSE of EB and showed that weighted jackknife methods have desirable asymptotic properties. The concept of this method is to put weights using hat matrix of auxiliary variables. Rao (2003) proposed a modification of jackknife method described in Jiang et al. (2002). This method leads to a computationally simpler jackknife estimator with an area-specific leading term. In the simulation study for Poisson responses, the relative bias of the area-specific jackknife estimator has been shown as the best MSE estimator in small number of areas for Poisson-Gamma model. For Poisson-Lognormal model, the relative bias of the weighted jackknife estimator has been shown as the best MSE estimator. Finnaly, this method was applied to estimate small area mean squared errors in disease mapping problems.