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Combined Estimators for Generalized Multiple Linear Models

In: Directional and Multivariate Statistics

Author

Listed:
  • Fidelis Ifeanyi Ugwuowo

    (University of Nigeria, Department of Statistics)

  • Kingsley Chinedu Arum

    (University of Nigeria, Department of Statistics)

  • Tobias Ejiofor Ugah

    (University of Nigeria, Department of Statistics)

Abstract

This study examines single and combined estimators in GLMs with restriction to multiple linear regression and Poisson regression models. We developed a combined estimator called Poisson robust PC-ridge by pooling principal component estimator with the ridge and transformed M-estimators in order to mitigate problems of multicollinearity and outliers in a Poisson Regression model (PRM). The properties of the Poisson robust PC-ridge (PRPCR) estimator were derived. We ascertained the efficiency of the (PRPCR) estimator via simulation study. The performance of (PRPCR) estimator with other single estimators like Poisson maximum likelihood estimator, Poisson ridge and Poisson jackknife ridge estimators were examined using mean squares error (MSE) as performance evaluation criterion. Poisson robust PC-ridge estimator outperformed the other estimators compared with in this study by having the smallest MSE. Poisson robust PC-ridge estimators’ performance shows that combined estimator is more efficient than single estimator in handling problems of mutlicollinearity and outliers individually and jointly in a GLM.

Suggested Citation

  • Fidelis Ifeanyi Ugwuowo & Kingsley Chinedu Arum & Tobias Ejiofor Ugah, 2025. "Combined Estimators for Generalized Multiple Linear Models," Springer Books, in: Somesh Kumar & Barry C. Arnold & Kunio Shimizu & Arnab Kumar Laha (ed.), Directional and Multivariate Statistics, pages 387-409, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-2004-3_20
    DOI: 10.1007/978-981-96-2004-3_20
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