Comparative Study of the Efficiency of Some Shrinkage Estimators on the Seemingly Unrelated Regression Model

Abstract

This study explored the efficiency of six different shrinkage estimators: Firinguetti , Alkhamisi and Shukur-Median , Alkhamisi and Shukur-Maximum , Hoerl and Kennard-Maximum , Hoerl et al-Harmonic mean , and Kibria on the Seemingly Unrelated Regression (SUR) model. A three-equation joint model was considered with different correlation levels among the explanatory variables (ρ_(x_i x_j )) and contemporaneous correlation levels (ρ_(ε_M )) among the equations. Samples sizes 20, 30, 50 and 100 replicated 10000 times in turn were considered for the simulation study. Results from the study revealed that the Trace Mean Square Error (TMSE) values for all the estimators decreased as the sample sizes increased when the different correlation levels among the explanatory variables were considered. When n = 20, ρ_(ε_M )= 0.9, the estimator R_AS had the best performance in terms of the TMSE criterion compared to the remaining estimators for all the cases of ρ_(x_i x_j ). When n = 30, ρ_(ε_M )= 0.9, the estimator R_SK had the best performance in terms of the TMSE criterion compared to the remaining estimators for ρ_(x_i x_j ) = 0.0, 0.9, while the estimator R_AS gave the best performance in terms of the TMSE criterion compared to the remaining estimators for ρ_(x_i x_j ) = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. When n = 50, ρ_(ε_M )= 0.9, the estimator R_SK had the best performance in terms of the TMSE criterion compared to the remaining estimators for ρ_(x_i x_j ) = 0.0, 0.1, 0.2, 0.3, 0.4, while the estimator R_AS had the best performance in terms of the TMSE criterion compared to the remaining estimators for ρ_(x_i x_j ) = 0.5, 0.6, 0.7, 0.8, 0.9. When n = 100, ρ_(ε_M )= 0.8, the estimator R_SK outperformed the other estimators in all cases except for ρ_(x_i x_j ) = 0.7, 0.8, 0.9. Conclusively, Alkhamisi and Shukur-Median outperformed other estimators, followed by Alkhamisi and Shukur-Maximum . Keywords: Multicollinearity, Ridge regression, Seemingly unrelated regression, Shrinkage estimators, Trace mean square error.