James-Stein type estimators in beta regression model: simulation and application

Abstract

Recently, the beta regression model has been used in several fields of science to model data in the form of rate or proportion. In this paper, some novel and improved methods to estimate parameters in the beta regression model are proposed. We consider a sub-space on the regression coefficients of the beta regression model and combine the unrestricted and restricted estimators then we present Stein-type and preliminary estimators. We develop the expressions for the proposed estimators' asymptotic biases and their quadratic risks. Numerical studies through Monte Carlo simulations are used to evaluate the performance of the proposed estimators in terms of their simulated relative efficiency. The results show that the proposed estimators outperform the unrestricted estimator when the restrictions hold. Finally, an empirical application is given to show how useful the proposed estimators are in the practical area.