Abstract
The Liu-type estimator is one of the shrink estimators that is used to remedy for a problem of multicollinearityin SUR model, but it is sensitive to the outlier. In this paper, we introduce the S Liu-type (SLiu-type) and MM Liu-type estimator (MMLiu-type) for SUR model. These estimators merge Liu-type estimator with S-estimator and with MM-estimator which makes it have high robustness at the different level of efficiency and at the same time prevents the bad effects of multicollinearity. Moreover, to get more robust features, we have modified the Liu-type estimator by making it depend on MM estimator instead of GLS estimator. The asymptotical properties for the suggested estimator were discussed and we used the fast and robust bootstrap (FRB) to obtain the suggested robust estimators. Furthermore, we run the simulation study to show the extent of excellence for the suggested robust estimators relative to the other estimators by many factors.
Highlights
The SUR model was introduced by Zellner in [27] which is a special case of the linear regression model
The Liu-Type estimator is the result of merging the ridge estimator and stein estimator and it has two parameters that work in parallel to effect the multicollinearity
This results clearly show that The MMLiu-Type and WMMliu-Type estimators work well when the other estimators at all factors and the Liu-Type estimator is the worst estimator at all factors
Summary
The SUR model was introduced by Zellner in [27] which is a special case of the linear regression model. Since the ridge parameter has instability, the Liu-type estimator, that was suggested by [12], is a suitable alternative for the ridge estimator. The Liu-Type estimator is the result of merging the ridge estimator and stein estimator and it has two parameters that work in parallel to effect the multicollinearity. The Liu-Type estimator for SUR model is calculated based on the following equation: minβ,Σ[(Y. [5] suggested robust ridge estimator for SUR model that merges ridge estimator with Sestimator that is calculated based on the following equation: min[log β,Σ. We introduce MM Liu-Type estimator for SUR model that merges Liu-Type estimator with MMestimator This estimator has a high breakdown point and is able to reduce the bad effect of multicollinearity at the same time
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