Sankhy¯a B: The Indian Journal of Statistics https://doi.org/10.1007/s13571-018-0171-4 c  2018, Indian Statistical Institute Liu-Type Multinomial Logistic Estimator Mohamed R. Abonazel Cairo University, Giza, Egypt Rasha A. Farghali Helwan University, Helwan, Egypt Abstract Multicollinearity in multinomial logistic regression affects negatively on the variance of the maximum likelihood estimator. That leads to inflated confi- dence intervals and theoretically important variables become insignificant in testing hypotheses. In this paper, Liu-type estimator is proposed that has smaller total mean squared error than the maximum likelihood estimator. The proposed estimator is a general estimator which includes other biased estimators such as Liu estimator and ridge estimator as special cases. Simu- lation studies and an application are given to evaluate the performance of our estimator. The results indicate that the proposed estimator is more efficient and reliable than the conventional estimators. AMS (2000) subject classification. Primary 62J07; Secondary 62J12. Keywords and phrases. Liu estimator, Multicollinearity problem, Optimal shrinkage parameter, Ridge regression estimator, Stepwise method. 1 Introduction Multicollinearity means that there is a near dependency between the explanatory variables in the regression models. In multinomial logistic re- gression (MLR) model, the maximum likelihood estimation method is used to obtain unbiased and efficient estimator of the regression parameters if the model not contains multicollinearity problem. However, the performance of maximum likelihood estimator (MLE) becomes poor when multicollinear- ity exists; in this case the MLE still unbiased but not efficient (has large variance). This leads to inflate the confidence intervals and theoretically important variables become insignificant in testing hypotheses. Applying biased estimators is a remedy to the negative results of multi- collinearity problem. Many shrinkage estimators are introduced to correct the multicollinearity problem in linear regression; such as ridge estimator by Hoerl and Kennard (1970a, b), Kibria (2003), Kibria and Banik (2016), Liu