On the Liu estimator in the beta and Kumaraswamy regression models: A comparative study

Abstract

Multi-collinearity among regressors and consequently ill-conditioning inflates the mean squared error (MSE) of the maximum likelihood estimator (MLE) of the parameters in a regression model. In recent years, the Liu estimator (LE) has been widely used in the literature to improve the regression models. Since in some regression models, the dependent variable follows a double bounded distribution, such as the beta and Kumaraswamy distributions, we are going to consider these two regression models in the presence of a multi-collinearity problem with investigation of their properties, characterizations, MLEs, and LEs. Finally, MSEs of LEs and MLEs are compared under various link functions, using simulation and two real data sets.

Keywords:

• Beta regression model
• Kumaraswamy regression model
• Liu estimator
• mean squared error
• maximum likelihood estimator
• multi-collinearity