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Beta regression: Shrinkage-Liu type Estimator with Application

Author

Listed:
  • Muhinyuza, Stanislas

    (Department of Economics and Statistics)

  • Karlsson, Peter

    (Department of Economics and Statistics)

  • Sahamkhadam, Maziar

    (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.

Suggested Citation

  • Muhinyuza, Stanislas & Karlsson, Peter & Sahamkhadam, Maziar, 2025. "Beta regression: Shrinkage-Liu type Estimator with Application," Working Papers in Economics and Statistics 6/2025, Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    • Handle: RePEc:hhs:vxesta:2025_006
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    References listed on IDEAS

    as
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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