Shrinkage and Penalty Estimators of a Poisson Regression Model |
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Authors: | Shakhawat Hossain Ejaz Ahmed |
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Affiliation: | 1. Department of Mathematics and Statistics, University of Winnipeg, , Winnipeg, MB, R3B 2E9 Canada;2. Department of Mathematics, Brock University, , L2S 3A1 Ontario, Canada |
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Abstract: | In this paper we propose Stein‐type shrinkage estimators for the parameter vector of a Poisson regression model when it is suspected that some of the parameters may be restricted to a subspace. We develop the properties of these estimators using the notion of asymptotic distributional risk. The shrinkage estimators are shown to have higher efficiency than the classical estimators for a wide class of models. Furthermore, we consider three different penalty estimators: the LASSO, adaptive LASSO, and SCAD estimators and compare their relative performance with that of the shrinkage estimators. Monte Carlo simulation studies reveal that the shrinkage strategy compares favorably to the use of penalty estimators, in terms of relative mean squared error, when the number of inactive predictors in the model is moderate to large. The shrinkage and penalty strategies are applied to two real data sets to illustrate the usefulness of the procedures in practice. |
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Keywords: | asymptotic distributional bias and risk likelihood ratio test Monte Carlo simulation penalty estimators Poisson regression shrinkage estimators |
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