The beta Liu-type estimator: simulation and application

Abstract

The Beta Regression Model (BRM) is commonly used while analyzing data where 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 the case that dependent variable follows a 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 in terms of 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.

Keywords

• Beta regression model
• Liu-type estimator
• maximum likelihood estimator
• multicollinearity

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