The Comparison of Two Methods Nonparametric Approach on Small Area Estimation (Case: Approach with Kernel Methods and Local Polynomial Regression)

Small Area estimation is a technique used to estimate parameters of subpopulations with small sample sizes. Small area estimation is needed in obtaining information on a small area, such as sub-districtor village. Generally, in some cases, small area estimation uses parametric modeling. But in fact, a lot of models have no linear relationship between the small area average and the covariate. This problemrequiresa non-parametric approach to solve, such as Kernel approach and Local Polynomial Regression(LPR).The purpose of this study is comparing the results of smaller estimation using Kernel approach hand LPR Data used in this study are generatedbysimulation resultsusing R language. Simulation data obtained by generating function m(x) are linear and quadratic pattern. The criteria used tocompare the results ofthe simulationare Absolute Relative Bias(ARB), MeanSquare Error(MSE), GeneralizedCross Validation(GCV), and risk factors. The simulation results showed: 1) Kernel gives smaller relative bias than LPR does on both linearandquadraticdata pattern. The relative bias obtained by Kernel tends to be more stable and consistent than the relative bias resulted by LPR, (2) the Kernel MSE is smaller than the LPR MSEeither on linear or quadratic pattern in any combination treatment, (3) the value of GCV and the risk factors in Kernel are smaller thanthe se in LPRin any combination of the simulated data patterns, (4) on nonparametric data, for both linear data patternandquadratic data pattern, Kernel methods provide better estimation compared to LPR.