Beta regression: Shrinkage-Liu type Estimator with Application

Beta regression has gained significant attention for modeling outcome variables bounded withinthe open interval from zero to one. In this paper, we introduce a two-parameter Liu linear shrinkageestimator tailored for estimating the vector of parameters in a Beta regression model with a fixeddispersion parameter, under the assumption of linear restrictions on the parameter vector. Thisestimator is particularly applicable in various practical scenarios where the level of correlation amongthe regressors varies, and the coefficient vector is suspected to belong to a linear subspace. Thenecessary and sufficient conditions for establishing the superiority of the new estimator over both oneparameterLiu estimators and two-parameter Stein-type estimators are derived in this paper. Finally,we conclude this paper by presenting two empirical applications that demonstrate the advantages ofutilizing the new estimator for applied researchers.