Modified Robust Method for Parameter Estimation of Multiple Regression Models
Keywords:
multiple regression, robust regression, S-estimatorAbstract
This research aimed to develop the parameter estimation by applying adjusted S-estimator and to compare the efficiency of parameter estimation by Mean Square Error (MSE) and the efficiency of forecasting by Mean Absolute Percentage Error (MAPE). The situations were simulated under 81 situations including 1) the error distributions are Standard Normal, Gamma and Weibull distribution, 2) the sample sizes are 20 60 and 100, 3) the percentage of outliers is 5, 25 and 40, and 4) the number of parameters is 2, 3 and 4. The research results demonstrated that: 1) the estimated parameters obtained from adjusted S-estimator are and unbiased parameters estimation of 2) The method of parameters estimation through adjusted S-estimator provided the value of MSE less than S-estimator from 59 situations. In most situations, the number of parameters is equal to 2 and 3 parameters. 3) The forecasting equation from the parameter estimation using adjusted S-estimator has the level of MAPE less than the level of MAPE of S-estimator from 41 situations which are mostly the Weibul distribution. The results of this research can be used as a guideline for selecting a robust parameter estimation of the multiple regression model when outliers occur with independent variables.
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