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Developing a First Order Two Parameter Estimator for Generalized Linear Models
Department of Statistics, Cukurova University, Adana, Turkey.
Department of Statistics, Cukurova University, Adana, Turkey.
Jönköping University, Jönköping International Business School, JIBS, Statistics.
2019 (English)In: 11th International statistics Congress ISC2019, Turkish Statistical Association and Giresun University , 2019Conference paper, Published paper (Refereed)
Abstract [en]

The generalized linear models were defined by Nelder and Wedderburn (1972) and these models allow us to fit regression models for univariate response data which follow a very common exponential family of distribution. The unknown regression coefficients of the generalized linear models are estimated by the maximum likelihood estimator. However, in the existence of multicollinearity, the variance of the maximum likelihood estimator becomes inflated and the statistical inferences based on the maximum likelihood method may not be reliable. In this study, we develop a first order two parameter estimator which combines the advantages of ridge and contraction estimators in the generalized linear models by extending the work of Özkale and Kaçıranlar (2007) in the linear model. The superiority of the first order two parameter estimator to the maximum likelihood, ridge and Liu estimators is investigated with regard to the mean square error criterion. We also examine some optimal estimators of biasing parameters. In addition to the theoretical comparisons, the performance of the estimators is judged by numerical evaluations where the mean square error is considered as a performance criterion.

Place, publisher, year, edition, pages
Turkish Statistical Association and Giresun University , 2019.
Keywords [en]
Generalized linear model, two parameter estimator, multicollinearity, first order approximation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-47706OAI: oai:DiVA.org:hj-47706DiVA, id: diva2:1390803
Conference
11th International statistics Congress ISC2019, 4 - 8 October 2019, Bodrum, Mugla, Turkey
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-03Bibliographically approved

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Qasim, Muhammad

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