Liu type estimator in cox proportional hazard regression model in presence of collinearity

Abstract

In this study, we will consider the liu type estimator in cox regression model. Generally maximum likelihood estimator is widely used to estimate cox regression model parameters. But this method can produce estimates having large mean squared error when predictor variables are multicollinear. For cox proportional hazard regression model, the ridge estimator has been applied as an alternative to the maximum likelihood estimator in presence of collinearity. According to the maximum likelihood estimator, the advantage of the ridge estimator is that former often has a smaller total mean squared error. Ridge regression combats the collinearity by using shrinkage parameter k. But especially when there exists high collinearity, the shrinkage parameter may not fully address the ill conditioning problem. To overcome this problem the liu type estimator which has two parameters is proposed. In this study, the liu type estimator for cox proportional hazard regression model will be obtained and compared to the ridge estimator in terms of mean squared error.