Almost unbiased ridge estimator in the count data regression models

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The Poisson regression negative binomial regression models are well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the count regression coefficients. To address this problem, a count data ridge estimator has been proposed by numerous researchers. In this paper, an almost unbiased regression estimator is proposed and derived. Our Monte Carlo simulation results suggest that the proposed estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the proposed estimator outperforms both negative binomial ridge regression and maximum likelihood estimators in terms of predictive performance.