Development of the Aslam-Ahmad estimator for the Cox proportional and hazards regression model with multicollinearity

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In the current article, we develop the Aslam-Ahmad estimator i.e. the modified Liu-ridge-type estimator as proposed by Aslam and Ahmad [Aslam M, Ahmad S. The modified Liu-ridge-type estimator: a new class of biased estimators to address multicollinearity. Commun Statist Simul Comput. 2022] for the Cox proportional hazards regression model. It is common to use the maximum partial likelihood approach for the parameter estimation of the Cox proportional hazards model. However, when there is considerable multicollinearity among the regressors, this estimator is unable to give stable estimates for the unknown regression coefficients. To vanquish the problem, the literature suggests many alternative biased estimators. Following this, we propose to tailor the Aslam-Ahmad estimator for the Cox proportional hazards model and define its properties. The performance of the proposed estimator with the available estimators has been evaluated by the Monte Carlo simulations using the scalar mean squared error criterion. A numerical example has also been provided for the illustration.