On linearized ridge logistic estimator in the presence of multicollinearity

Logistic Regression is a very popular method to model the dichotomous data. The maximum likelihood estimator (MLE) of unknown regression parameters of the logistic regression is not too accurate when multicollinearity exists among the covariates. It is well known that the presence of multicollinearity increases the variance of the MLE. To diminish the inflated mean square error (MSE) of the MLE due to the presence of multicollinearity, we proposed a new estimator designated as linearized ridge logistic estimator. The conditional superiority of the proposed estimator over the other existing estimators is derived theoretically and the optimal choice of shrinkage parameter is suggested. Monte Carlo simulations are performed to study the performance of the proposed estimator through MSE sense. Also, a numerical example is presented to support the results.