Department of Quantitative Methods

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Browsing Department of Quantitative Methods by Subject "Estimators when the collinearity"

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    Performance assessment of some existing and new ridge regression estimators
    (University of Management and Technolog, 2017) Himmad Khan
    An important assumption of the multiple linear regression model is that the regressors should be independent, which is violated in practice. Due to violation of this assumption, the problem of multicollinearity occurs and results into unreliable statistical inference for the model parameters. To cope this, several biased estimation techniques, including ridge regression, have been proposed in the literature. In ridge regression, the key problem is to estimate the ridge parameter and there are several methods in the literature for this purpose. In this thesis, we propose six different shrinkage estimators, named as HMS1 to HMS6 and further compare them to some existing methods, like HK, KMS, KSM, KMED and KGM. We use Monte Carlo simulations to assess the performance of different estimators assuming the mean square error as a performance comparison criterion. In particular, we assess the performance assuming various choices of error distribution, error variance, the correlation among the predictors, the sample size and the number of predictors. In addition to simulation study, we also analyze a real life example for the comparison of different estimators. On the basis of simulation study and real data example, we found that our new proposed estimators outperform in most of the assumed conditions, especially when the error distribution is Normal, level of collinearity, variance between errors and predictors were moderate to high. However, it was also observed that the estimators KMS, KSM and HMS1 performed better than other estimators when the collinearity and error variance were small or moderate. when the error distribution is students-t , we observed that the estimators KGM, KMS, HMS1 and HMS5 outperformed among others. Moreover, we noticed that for high level of collinearity, and different values of variance of error terms, the HMS5 outperformed among others.