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The objective of this research is to compare the efficiency of coefficient parameter estimation by using penalized regression analysis on five methods namely the ridge regression, the lasso regression, the elastic net regression, the adaptive lasso regression, and the adaptive elastic net regression methods. This research uses the multiple linear regression model, which is consisted of a dependent variable and independent variables. In case the number of independent variables is larger than number of sample sizes called high-dimensional data. For comparison the efficiency of five methods, the criterion is based on the average mean square errors. The data of this research is simulated by the small sample sizes ( = 5, 10, and 15) when the number of independent variables is specified by 16. For medium sample sizes ( = 20, 30, and 40), the number of independent variables is specified by 50. For large sample sizes ( = 60, 70, and 80), the number of independent variables is defined 100. The independent variable distribution is generated from the normal distribution, and the residuals are generated from the normal distribution, contaminated normal distribution, and Weibull distribution The data are obtained through simulation using a Monte Carlo technique with 1,000 replications for each case. The results are found that the adaptive elastic net regression is the minimum average mean square error in all cases. Furthermore, we apply five methods for real data based on the small sample sizes when the number of independent variables is considered on 16. The results of real data show that the adaptive elastic net regression outperforms the other methods as the simulation data.
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