A unified approach to outlier and collinearity problems: Robust Jackknifed beta regression

Abstract

The beta regression model is crucial for analyzing fractional data restricted to (0, 1), yet its maximum likelihood estimator is highly susceptible to multicollinearity and outliers, leading to unstable and unreliable parameter estimates. To address this critical dual challenge, this paper proposes an enhanced Robust Jackknifed Beta Regression Estimator for the beta regression model. The core innovation lies in the derivation of a new optimal bias parameters (k and d) selection criterion that effectively balances the variance inflation from collinearity against the influence of extreme observations. We performed simulation and real-data studies to investigate its performance. A comprehensive Monte Carlo simulation evaluates the Robust Jackknifed Beta Regression’s finite-sample performance in terms of simulated mean squared error and influence ratio under varying degrees of multicollinearity and outlier contamination. The numerical results confirm that the proposed robust Jackknifed two-parameter estimator offers significantly more robust and stable parameter estimates than its competitors (maximum likelihood estimator, robust Jackknifed Liu estimator, robust two-parameter estimator, Jackknifed two-parameter estimator especially in the presence of both severe collinearity and influential outliers. In addition to the simulation evidence, we establish the theoretical dominance of the robust Jackknifed two-parameter estimator over all competing estimators in the matrix mean squared error sense, proving that the proposed estimator achieves strictly lower mean sqaure error under both clean and contaminated data conditions. The simulation results are fully consistent with these theoretical findings.

Keywords

• Beta regression
• collinearity
• Jackknife
• outlier
• robust

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