Restricted Liu estimator under stochastic linear restrictions in generalized linear models: theory and applications

It is a fact that the problem of multicollinearity adversely effects the estimation of parameters not only in normal linear models but also in generalized linear models (GLMs). In this study, we propose a new estimator by imposing the stochastic restrictions on the parameters and combining the Liu estimator in GLMs to address the problem of multicollinearity. The new estimator is referred to as the stochastic restricted Liu estimator. The novel estimator's first order approximated form (FOA) is presented to compare it to its competitors using the asymptotic mean square error criterion. Furthermore, two empirical applications using a response variable from the Poisson and Gamma distributions are studied to evaluate the performance of estimators. In addition, a simulation study is conducted by considering a response variable from Binomial distribution for comparisons. Based on simulation study and empirical applications, it is found that the performance of the proposed estimator is better than ML, Liu, and mixed estimators for the appropriate selected biasing parameter.