The \(r\)-\(k\) class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. (English) Zbl 1488.62116
Summary: 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.
MSC:
| 62J12 | Generalized linear models (logistic models) |
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
| 62F10 | Point estimation |
| 62H25 | Factor analysis and principal components; correspondence analysis |
Keywords:
maximum likelihood estimator; principal component regression; ridge estimator; \(r\)-\(k\) class estimator; reduction rate; Gamma; Poisson dataReferences:
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