Jackknifed estimators for generalized linear models with multicollinearity

Generalized linear models applications have become very popular in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. In this paper, we introduce a new Jackknifed two-parameter estimator and a new modified Jackknifed two-parameter estimator in the case of Poisson, negative binomial and gamma distributed response variables in generalized linear models. We examine bias vectors, covariance matrices, and matrix mean squared error of the Jackknifed ridge estimator, modified Jackknifed ridge estimator, Jackknifed Liu estimator, modified Jackknifed Liu estimator, Jackknifed Liu-type estimator and modified Jackknifed Liu-type estimator given in the literature. According to bias vectors and covariance matrices, the superiority of the Jackknifed two-parameter estimator has been demonstrated theoretically. The generalization of some estimation methods for ridge and Liu parameters in generalized linear models is provided. Also, the superiority of the Jackknifed two-parameter estimator and the modified Jackknifed two-parameter estimator are assessed by the simulated mean squared error via Monte-Carlo simulation study where the response follows a Poisson, negative binomial, and gamma distribution with the log link function. Finally, we consider real data applications. The proposed estimators are compared and interpreted.