Performance of a New Restricted Biased Estimator in Logistic Regression

Abstract

It is known that the variance of the maximum likelihood estimator (MLE) inflates when the explanatory variables are correlated. This situation is called the mul-ticollinearity problem. As a result, the estimations of the model may not be trustful. Therefore, this paper introduces a new restricted estimator (RLTE) that may be applied to get rid of the multicollinearity when the parameters lie in some linear subspace in logistic regression. The mean squared errors (MSE) and the matrix mean squared errors (MMSE) of the estimators considered in this paper are given. A Monte Carlo experiment is designed to evaluate the performances of the proposed estimator, the restricted MLE (RMLE), MLE and Liu-type estimator (LTE). The criterion of performance is chosen to be MSE. Moreover, a real data example is presented. According to the results, proposed estimator has better performance than MLE, RMLE and LTE.