BOOTSTRAP PARAMETRIK DAN NONPARAMETRIK UNTUK PENDUGAAN KUADRAT TENGAH GALAT DALAM STATISTIK AREA KECIL DENGAN RESPON BERSEBARAN LOGNORMAL

Abstract

Small area estimation is needed to obtain information in small area, that is area containing small size of sample. Direct estimation in small area will result in large variance. Indirect estimation is the solution, with involves auxiliary data from related area or another survey in parameter estimation. One of the prolems found in using this procedure is low precision of Mean Square Error (MSE) estimate caused by non-normal distribution. Parameter of concern in this study is per capita expenditure of village in Bogor regency. Per capita expenditure is non-normal distribution. MSE estimator with bootstrap method has the advantage of potential robustness against sampling from non- normal distribution. Therefore this study used bootstrap method, such as parametric bootstrap and nonparametric bootstrap, in MSE estimation. Generally, the result showed that the MSE estimate of the parametric bootstrap smaller than the nonparametric bootstrap. Both method have better precision, so that they can repair the result of direct estimation.
Keywords : small area estimation, parametric bootstrap, nonparametric bootstrap