A generalized Liu-type estimator for logistic partial linear regression model with multicollinearity

This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results.

Automated summary

This paper introduces a generalized Liu-type estimator (GLTE) to address the multicollinearity problem in the logistic partially linear regression model. The GLTE is derived using the profile likelihood method and it includes several existing estimators as special cases. The superiority of GLTE over other estimators is demonstrated and optimal choices for biasing parameters are provided. Numerical simulations show that GLTE outperforms existing estimators, and an application on real data is presented.