The Poisson Regression Model (PRM) is commonly used in applied sciences such as economics and the social sciences when analyzing the count data. The maximum likelihood method is the well-known estimation technique to estimate the parameters in PRM. However, when the explanatory variables are highly intercorrelated, unstable parameter estimates can be obtained. Therefore, biased estimators are widely used to alleviate the undesirable effects of these problems. In this study, a new improved Liu-type estimator is proposed as an alternative to the other proposed biased estimators. The superiority of the new proposed estimator over the existing biased estimators is given under the asymptotic matrix mean square error criterion. Furthermore, Monte Carlo simulation studies are executed to compare the performances of the proposed biased estimators. Finally, the obtained results are illustrated in real data. Based on the set of experimental conditions which are investigated, the proposed biased estimator outperforms the other biased estimators.

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The Beta Regression Model (BRM) is commonly used when analyzing data in which the dependent variable is restricted to the interval [0,1] for example proportion or probability. The Maximum Likelihood Estimator (MLE) is used to estimate the regression coefficients of BRMs. But in the presence of multicollinearity, MLE is very sensitive to high correlation among the explanatory variables. For this reason, we introduce a new biased estimator called the Beta Liu-Type Estimator (BLTE) to overcome the multicollinearity problem in which the dependent variable has Beta distribution. The proposed estimator is a general estimator which includes other biased estimators, such as the Ridge Estimator, Liu Estimator, and the estimators with two biasing parameters as special cases in BRM. The performance of the proposed new estimator is compared to the MLE and other biased estimators depending on the Estimated Mean Squared Error (EMSE) criterion by conducting a simulation study. Finally, a numerical example is given to show the benefit of the proposed estimator over existing estimators.

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The Poisson Regression Model (PRM) is one of the benchmark models when analyzing the count data. The Maximum Likelihood Estimator (MLE) is used to estimate the model parameters in PRMs. However, the MLE may suffer from various drawbacks that arise due to the existence of multicollinearity problems. Many estimators have been proposed as alternatives to each other to alleviate the multicollinearity problem in PRM, such as Poisson Ridge Estimator (PRE), Poisson Liu Estimator (PLE), Poisson Liu-type Estimator (PLTE), and Improvement Liu-Type Estimator (ILTE). In this study, we define a new general class of estimators which is based on the PRE as an alternative to other existing biased estimators in the PRMs. The superiority of the proposed biased estimator over the other existing biased estimators is given under the asymptotic matrix mean square error sense. Furthermore, two separate Monte Carlo simulation studies are implemented to compare the performances of the proposed biased estimators. Finally, the performances of all considered biased estimators are shown in real data.