Logistic Liu Estimator under stochastic linear restrictions

Abstract

In order to overcome the problem of multicollinearity in logistic regres sion, several researchers proposed alternative estimators when exact linear restrictions are available in addition to sample model. However, in practical situations the linear restrictions are not always exact and mostly their nature is stochastic. In this paper, we propose a new estimator called stochastic restricted Liu maximum likelihood estimator (SRLMLE) by incorporating Liu estimator to the logistic regression model when the linear restrictions are stochastic. Moreover, the conditions for superiority of SRLMLE over the maximum likelihood estimator (MLE), stochastic restricted maximum like lihood estimator (SRMLE) and restricted Liu logistic estimator (RLLE) are derived with respect to mean square error criterion. Finally, the performance of the new esti mator over MLE, LLE, SRMLE and RLLE is investigated in the sense of scalar mean squared error by conducting a Monte Carlo simulation and using a numerical example.