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, ‎we propose some novel and improved methods to estimate parameters in the beta regression model‎. ‎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 provided to demonstrate the practical usefulness of the proposed ‎estimators.‎