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Enhancing gamma regression models through the integration of principal component regression and the Stein estimator
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DOI：10.1080/02286203.2026.2690149.png)
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Abstract
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We propose a shrinkage estimator for gamma regression models that combines principal component dimension reduction with a Stein-type adjustment. In the presence of multicollinearity, the maximum likelihood estimator can exhibit substantial variance inflation, motivating the use of biased alternatives. The proposed estimator applies a Stein-type shrinkage rule to the principal component regression estimator, thereby integrating dimension reduction and risk reduction within a unified framework. We derive its analytical properties, establish conditions under which it dominates the maximum likelihood estimator under scalar mean squared error, and characterize its risk behavior relative to existing biased estimators. Finite-sample performance is investigated through Monte Carlo experiments across varying correlation structures and sample sizes. An empirical application illustrates the practical implications of the method. The results demonstrate that combining principal component regression with Stein-type shrinkage yields systematic risk improvements in gamma regression under multicollinearity.
Keywords:
Gamma regression model
multicollinearity
principal component regression
Stein estimator
ridge regression
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