THE COMPARISON OF TWO METHOD NONPARAMETRIC APPROACH ON SMALL AREA ESTIMATION (CASE: APPROACH WITH KERNEL METHODS AND LOCAL POLYNOMIAL REGRESSION)

Subject Areas : International Journal of Mathematical Modelling & Computations

Dewi Ratnaningsih ¹ (Indonesia)

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

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Abstract :

Small Area estimationis a technique used to estimate parameters of subpopulationswithsmallsamplesizes. Small area estimation is needed in obtaining information on a small area,suchas sub-districtor village. Generally, in some cases, small area estimation usesparametric modeling. But in fact, a lot of models haveno linear relationship betweenthesmall area average andthecovariate.This problemrequiresanon-parametric approachto solve, such asKernel approach and LocalPolynomialRegression (LPR).The purpose of thisstudyis comparing the results ofsmall area estimation using Kernel approach andLPR.Data usedin this study aregeneratedby simulation results using R language . Simulation data obtained by generating function m (x) are linear and quadratic pattern. The criteria used to compare the results of the simulation are Absolute Relative Bias (ARB), Mean Square Error (MSE), Generalized Cross Validation (GCV), and risk factors.The simulation resultsshowed: 1)Kernel gives smaller relative bias than LPR does on bothlinearand quadratic data pattern.The relativebiasobtained by Kerneltends to be more stable and consistent than the relative biasresulted byLPR, (2) the Kernel MSE is smaller thantheLPRMSEeither onlinear or quadratic pattern in any combination treatment, (3) the value of GCV andtherisk factors inKernelaresmaller thanthese inLPRin anycombination of the simulated data patterns, (4) on non parametric data, forboth linear data patternandquadraticdata pattern, Kernelmethods provide better estimationcompared to LPR.