负二项回归模型下双参数估计的有效性研究

he negative binomial (NB) regression model，a typical generalized linear regression models,is very popular in applied research when analyzing count data. A new two-parameter estimator is proposed in order to solve the problem of an inflated mean square error (MSE) of the classical maximum likelihood (ML) method in the presence of multicollinearity. The proposed two-parameter estimator is a general estimator which includes the ML estimator, the ridge estimator and the Liu estimator as special cases. Some properties on the asymptotic MSE are derived and the necessary and sufficient conditions for the superiority of the new two-parameter estimator over the ML estimator are done in the mean square error matrix (MSEM) sense . Furthermore, selections of the biasing parameters are discussed and a Monte Carlo simulation study is given to illustratesome of the theoretical results.