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According to existing literature, the ordinary least squares (OLS) estimators are not the best in presence of multicollinearity. The inability of OLS estimators against multicollinearity has paved the way for the development of various ridge type estimators for circumventing the problem of multicollinearity. In this paper improved two-parameter ridge (ITPR) estimators are proposed. A simulation study is used to evaluate the performance of proposed estimators based on minimum mean squared error (MSE) criterion. The simulative results reveal that, based on minimum MSE, ITPR2 was the most efficient estimator compared to the considered estimators in the study. Finally, a real-life dataset is analyzed to demonstrate the applications of the proposed estimators and also checked their efficacy for mitigation of multicollinearity. [ABSTRACT FROM AUTHOR]

Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models. [ABSTRACT FROM AUTHOR]

AbstractRegression analysis is widely used to predict the response variable utilizing one or more predictor variables. In many fields of study, the predictors are highly correlated causing multicollinearity problem that severely affects the efficiency of ordinary least square (OLS) estimators by significantly inflating their variances. To solve the multicollinearity problem, various one and two parameter ridge estimators are available in literature. In this article, a class of modified two parameter Lipovetsky–Conklin ridge estimators is proposed based on eigen values of X′X matrix that provide an automatic dealing option for treating different levels of multicollinearity. An extensive simulations study followed by real life example is used to evaluate the performance of proposed estimators based on MSE criterion. In most of the simulation conditions, our proposed estimators outperformed the existing estimators. [ABSTRACT FROM AUTHOR]

The inability of ordinary least square estimators against multicollinearity has paved the way for the development of various ridge-type estimators, which are recently classified as one-parameter and two-parameter ridge estimators. In this paper, we offer some efficient two-parameter ridge estimators and evaluate their performance through a simulation study by using the minimum mean square error criterion. Under most of the simulation conditions, our proposed estimators outperformed the existing estimators. Finally, two real-life datasets are used to demonstrate the applications of our proposed estimators. [ABSTRACT FROM AUTHOR]