The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses
| Autor: | Atıf Abbasi, Revan Özkale |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Generalized linear model
Statistics and Probability Class (set theory) Algebra and Number Theory maximum likelihood estimator principal component regression ridge estimator r-k class estimator reduction rate Gamma Poisson data Scalar (physics) Estimator Poisson distribution symbols.namesake Empirical research Multicollinearity symbols Applied mathematics Principal component regression İstatistik ve Olasılık Geometry and Topology Analysis Mathematics |
| Zdroj: | Volume: 50, Issue: 2 594-611 Hacettepe Journal of Mathematics and Statistics |
| ISSN: | 2651-477X |
| Popis: | Multicollinearity is considered to be a significant problem in the estimation of parameters not only in general linear models, but also in generalized linear models (GLMs). Thus, in order to alleviate the serious effects of multicollinearity a new estimator is proposed by combining the ridge and PCR estimators in GLMs. This new estimator is called the r-k class estimator in GLMs. The various comparisons of the new estimator are made with already existing estimators in the literature, which are maximum likelihood (ML) estimator, ridge and PCR estimators, respectively. The comparisons are to be made in terms of scalar MSE criterion. So that, a numerical example and application through simulation are mentioned in the study for Poisson and Gamma response variables, respectively. On the basis of results it is found that, the proposed estimator outperforms all of its competitors comprehensively. |
| Databáze: | OpenAIRE |
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