When the multicollinearity exists in linear regression model, the result of the Restricted Least Square estimator (RLS) is unstable. So that, more researchers proposed the restricted biased estimators to improve the efficiency of RLS estimator. In this paper, Some of biased restricted estimators have been introduced to study the performance of them. The simulation study has been given to compare these estimators. According to simulation study, we found that, the shrinkage restricted ridge regression (SRRE) estimator which proposed by Baber and Mustafa [1], has good properties comparing with other restricted estimators that given in this study. A Numerical example has been considered to illustrate the performance of these estimators
More researchers used biased estimators instead of the restricted least square estimator (RLS) that is unbiased to improve the efficiency of the estimator. Therefore, in this paper, we proposed new biased estimator, called restricted modified unbiased ridge regression (RMUR) based on modified unbiased ridge regression (MURR) that suggested by Batah and Gory (2009). By some theorems and a simulation study, we show that, this new estimator has desirable properties as the MUR and it is better than the RLS. A numerical example from literature is used to illustrate the results.
In the linear regression model, the restricted biased estimation as one of important methods to addressing the high variance and the multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison among them. According to the simulation study we observe that, the performance of the restricted modified unbiased ridge regression estimator (RMUR) was proposed by Bader and Alheety (2020) is better than of these estimators. Numerical example have been considered to illustrate the performance of the estimators.
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