Leverage and influential observations on the restricted Liu estimator in the linear mixed measurement error models

Document Type : Original Scientific Paper

Author

Department of Mathematics and Statistics‎, ‎Sho.C.‎, ‎Islamic Azad University‎, ‎Shoushtar‎, ‎Iran

Abstract

A fundamental step in constructing linear regression models is the identification of atypical observations, specifically high-leverage and influential points. The coexistence of atypical observations and severe multicollinearity complicates statistical analysis and reduces the effectiveness of conventional diagnostic methods. To address these challenges, this paper proposes diagnostic methods based on the restricted Liu estimator for identifying atypical observations in linear mixed measurement error models. Specifically, generalized leverage matrices are derived using the restricted Liu estimator to identify high-leverage points. Furthermore, several case-deletion measures are developed based on the restricted Liu estimator to serve as robust tools for diagnosing influential points. The performance of the proposed methods is evaluated through two simulation studies and an application to a real-life example.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 6, Issue 2
July 2025
Pages 137-151

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History

  • Receive Date: 17 November 2025
  • Revise Date: 14 May 2026
  • Accept Date: 12 August 2026

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