Working Papers in Economics and Statistics,
Linnaeus University, School of Business and Economics, Department of Economics and Statistics

Abstract: Beta regression has gained significant attention for modeling outcome variables bounded within the open interval from zero to one. In this paper, we introduce a two-parameter Liu linear shrinkage estimator tailored for estimating the vector of parameters in a Beta regression model with a fixed dispersion parameter, under the assumption of linear restrictions on the parameter vector. This estimator is particularly applicable in various practical scenarios where the level of correlation among the regressors varies, and the coefficient vector is suspected to belong to a linear subspace. The necessary and sufficient conditions for establishing the superiority of the new estimator over both one-parameter Liu 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 of utilizing the new estimator for applied researchers.

Keywords: Beta regression model; Linear restrictions; Liu estimator; Matrix mean square error; Two parameter Liu linear shrinkage estimator; Stein-type estimator

JEL-codes: C02; C13; C18; C46

Language: English

12 pages, December 30, 2025

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