Regression analysis

Minimum-variance unbiased estimator

Multicollinearity

Mathematics

Statistics

Mean squared error

Estimator

Variance inflation factor

Bias of an estimator

Efficient estimator

Frontiers in Applied Mathematics and Statistics

The beta regression is a widely known statistical model when the response (or the dependent) variable has the form of fractions or percentages. In most of the situations in beta regression, the explanatory variables are related to each other which is commonly known as the multicollinearity problem. It is well-known that the multicollinearity problem affects severely the variance of maximum likelihood (ML) estimates. In this article, we developed a new biased estimator (called a two-parameter estimator) for the beta regression model to handle this problem and decrease the variance of the estimation. The properties of the proposed estimator are derived. Furthermore, the performance of the proposed estimator is compared with the ML estimator and other common biased (ridge, Liu, and Liu-type) estimators depending on the mean squared error criterion by making a Monte Carlo simulation study and through two real data applications. The results of the simulation and applications indicated that the proposed estimator outperformed ML, ridge, Liu, and Liu-type estimators.

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application