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The iterative restricted r−k class estimator with exact linear restrictions in generalized linear models: theory, simulation and application.

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Title: The iterative restricted r−k class estimator with exact linear restrictions in generalized linear models: theory, simulation and application.
Authors: Abbasi, Atif1 (AUTHOR) atif.abbasi@ajku.edu.pk, Kibria, B. M. Golam2 (AUTHOR)
Source: Communications in Statistics: Simulation & Computation. Apr2025, p1-19. 19p.
Subject Terms: *SIMULATION methods & models, POISSON regression, MAXIMUM likelihood statistics, REGULARIZATION parameter, MEAN square algorithms, PREDICTION models
Abstract: AbstractIn this paper, we propose a restricted r−k class estimator for generalized linear models (GLMs), which, under certain conditions, includes other estimators as specific cases. We provide four distinct estimates for selecting the shrinkage parameter k. The proposed estimator is compared with the Maximum Likelihood (ML) estimator using the mean square error (MSE) matrix criterion. Additionally, we perform two simulation studies and analyze two numerical examples to assess the performance of the estimators for Poisson and negative binomial regressions, respectively. The performance evaluation criteria employed are the scalar mean square error (SMSE) and the estimated mean square error (EMSE). According to our results, the proposed restricted r−k class estimator performs better than the ML estimator in the numerical examples, regardless of the shrinkage parameter k values. However, it performs better across all scenarios considered in the simulation studies, with the exception of the case when ρ2=0.80 and n=100, where k is found using kGM. [ABSTRACT FROM AUTHOR]
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Database: Business Source Index
Description
Abstract:AbstractIn this paper, we propose a restricted r−k class estimator for generalized linear models (GLMs), which, under certain conditions, includes other estimators as specific cases. We provide four distinct estimates for selecting the shrinkage parameter <italic>k</italic>. The proposed estimator is compared with the Maximum Likelihood (ML) estimator using the mean square error (MSE) matrix criterion. Additionally, we perform two simulation studies and analyze two numerical examples to assess the performance of the estimators for Poisson and negative binomial regressions, respectively. The performance evaluation criteria employed are the scalar mean square error (SMSE) and the estimated mean square error (EMSE). According to our results, the proposed restricted r−k class estimator performs better than the ML estimator in the numerical examples, regardless of the shrinkage parameter <italic>k</italic> values. However, it performs better across all scenarios considered in the simulation studies, with the exception of the case when ρ2=0.80 and n=100, where <italic>k</italic> is found using kGM. [ABSTRACT FROM AUTHOR]
ISSN:03610918
DOI:10.1080/03610918.2025.2495278