To circumvent the problem of multicollinearity, biased estimation method has been suggested to improve the precision of estimators. In this paper, we study types of biased estimators that can help to reduce the effect of multicollinearity on estimation. A simulation study is carried out to study the relative effectiveness of certain types of biased estimators in comparison to some proposed estimated ridge parameter (k) that have been shown in the literature . Moreover, a real data set has been considered to support the simulation results based on the estimated mean square error criterion.
In linear regression model, the biased estimation is one of the most commonly used methods to reduce the effect of the multicollinearity. In this paper, a simulation study is performed to compare the relative efficiency of some kinds of biased estimators as well as for twelve proposed estimated ridge parameter (k) which are given in the literature. We propose some new adjustments to estimate the ridge parameter. Finally, we consider a real data set in economics to illustrate the results based on the estimated mean squared error (MSE) criterion.
According to the results, all the proposed estimators of (k) are superior to ordinary least squared estimator (OLS), and the superiority among them based on minimum MSE matrix will change according to the sample under consideration.
In this research, two types of bias estimator were studied in linear regression model which are; (almost unbiased generalized ridge estimator, almost unbiased two-parameter estimator and Modified ridge-type estimator) and (The (r-k) class estimator and modified (r-k) class ridge regression estimator) as a method of repressing the multicollinearity problem on parameter estimation in multiple linear regression models. Also, a simulation analysis was used to test the relative efficiency of certain types of biased estimators as well as the thirty-nine proposed estimated ridge parameters (k) that have been shown in the literature. Moreover, the mean square error was also assigned to study the quality of those estimators in different circumstances and for different correlations. Finally, a practical example was applied to illustrate the obtained results. All proposed estimators of (k) are, according to the results, superior to ordinary least squared estimator (LSE), but there is no ‘optimal’ estimator guarantee that can come out, and the best estimator option will depend on the study conditions.
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