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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 3

The $r$-$d$ class estimator under exact linear restrictions in generalized linear models: Theory, simulation and application

Atıf Abbası(The University of Azad Jammu and Kashmir Muzaffarabad)0000-0001-9987-0193
Revan Özkale(CUKUROVA UNIVERSITY)0000-0001-7085-7403
Pages
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Publication Date
2025-06-24
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results indicate that the proposed estimator consistently outperforms all competing estimators considered in this study, both in simulation experiments and the numerical example, for suitably chosen values of the biasing parameter $ d $.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we propose a restricted $r-d$ class estimator in generalized linear models by combining Liu and Principal component regression estimators, when exact linear restrictions are available as prior information along with the sample data.
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Key Findings & Data:The performance of the proposed estimators is examined through simulation studies and a numerical example, considering response variables that follow Poisson, Binomial, and Negative binomial distributions.
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Conclusion & Impact:The results indicate that the proposed estimator consistently outperforms all competing estimators considered in this study, both in simulation experiments and the numerical example, for suitably chosen values of the biasing parameter $ d $.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Exact restrictions · logistic regression · mean square error

Abstract

In this paper, we propose a restricted $r-d$ class estimator in generalized linear models by combining Liu and Principal component regression estimators, when exact linear restrictions are available as prior information along with the sample data. In addition, Particle Swarm Optimization is introduced and utilized to estimate the biasing parameter $ d $ of the newly constructed restricted estimator. In the presence of multicollinearity problem, the new estimator is compared with the current estimators that are maximum likelihood, principal components regression and $r-d$ class estimators, respectively. The performance of the proposed estimators is examined through simulation studies and a numerical example, considering response variables that follow Poisson, Binomial, and Negative binomial distributions. The evaluation is based on the scalar mean square error and the estimated mean square error criteria. The results indicate that the proposed estimator consistently outperforms all competing estimators considered in this study, both in simulation experiments and the numerical example, for suitably chosen values of the biasing parameter $ d $.

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Cite This Article

Abbası, A., Özkale, R. (2025). The $r$-$d$ class estimator under exact linear restrictions in generalized linear models: Theory, simulation and application. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 3. https://doi.org/10.15672/hujms.1638426

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