The logistic regression model is used when the response variables are dichotomous. In the presence of multicollinearity, the variance of the maximum likelihood estimator (MLE) becomes inflated. The Liu estimator for the linear regression model is proposed by Liu to remedy this problem. Urgan and Tez and Mansson et al. examined the Liu estimator (LE) for the logistic regression model. We introduced the restricted Liu estimator (RLE) for the logistic regression model. Moreover, a Monte Carlo simulation study is conducted for comparing the performances of the MLE, restricted maximum likelihood estimator (RMLE), LE, and RLE for the logistic regression model.

Two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing parameters intends to gain a remedial impact for multicollinearity. Within this respect, we define a new TP estimator to eliminate the disorder originated from multicollinearity. Also, we perform theoretical comparisons for new TP estimator according to mean square error criterion. By minimizing the mean square error, we derive optimal estimators for both of the biasing parameters of this new estimator. Moreover, we recommend a mathematical programming approach to determine two biasing parameters, simultaneously. In this approach, we minimize the mean square error and improve the length of the newly defined TP estimator. In application part, computations regarding the estimations of the biasing parameters and mean square errors, and the length of the estimated coefficients are examined.

Multicollinearity is often ignored in censored regression model. In this respect, Tobit Liu estimation is proposed as an alternative in order to dispel the adverse effects of multicollinearity on the maximum likelihood estimation. Tobit Liu estimator is compared with Tobit ridge estimator and Tobit maximum likelihood estimator, theoretically via mean square error. For empirical analysis, we prefer Mroz dataset which is a phenomenon in the context of censored regression. Since many studies have investigated Mroz dataset by neglecting multicollinearity, we handle this dataset in the context of multicollinearity in this paper. Moreover, it is seen that multicollinearity is not included in pioneer studies' simulation designs. Therefore, we conduct a Monte Carlo simulation study where we take account of different levels of multicollinearity while generating data. Briefly, this study contributes to filling an important gap in the literature and proposes to investigate other econometrically censored data in the context of multicollinearity.