Advances and Applications in Statistics
Volume 52, Issue 6, Pages 375 - 389
(June 2018) http://dx.doi.org/10.17654/AS052060375 |
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WEIGHT LAD AND WEIGHT LAD RIDGE ESTIMATOR FOR SEEMINGLY UNRELATED REGRESSION MODELS
Tarek M. Omara
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Abstract: In this paper, we introduce the four new estimators for seemingly unrelated regression (SUR) model, viz., weight least absolute deviations (WLAD), general weight least absolute deviations (WGLAD), weight least absolute deviations ridge (WLAD_Ridge) and general weight least absolute deviations ridge (GWLAD_Ridge) estimator. The LAD and GLAD estimators are sensitive to the leverage point, so the WLAD and WGLAD are suitable alternatives to deal with this problem. On the other hand, the ridge estimator is used when the predictors are highly collinear. The weight least absolute deviations ridge (WLAD_Ridge) and general weight least absolute deviations ridge (GWLAD_Ridge) estimators combine the interesting features of weight least absolute deviations (WLAD) and ridge estimators. The aim of these estimators is to resist the outliers, leverage point and at the same time shrinking coefficient to solve the multicollinearity simultaneously in SUR model. We chose ridge parameter by the new robust criteria, least absolute deviations (LAD) cross validation criteria. We drove the simulation study of WLAD, WGLAD, (WLAD_Ridge) and (GWLAD_Ridge) estimators to determine the efficiency gain for it and to compare with the other estimators. |
Keywords and phrases: seemingly unrelated regression (SUR), weight least absolute deviations (WLAD), general weight least absolute deviations (GWLAD), weight least absolute deviations ridge (WLAD_Ridge), general weight least absolute deviations ridge (GWLAD_Ridge), least absolute deviations (LAD) cross validation criteria. |
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