Gamma回归模型的几乎无偏岭估计

Almost Unbiased Ridge Estimation for Gamma Regression Model

针对Gamma回归模型的复共线性,文章提出Gamma回归模型的几乎无偏岭估计。研究了几乎无偏岭估计与极大似然估计之间的线性关系,证明了几乎无偏岭估计是一种压缩估计。在均方误差准则下,讨论了几乎无偏岭估计的均方误差关于参数k的函数性质,并给出了几乎无偏岭估计优于极大似然估计和普通岭估计的存在性定理。最后讨论了最优几乎无偏岭参数的一种取值方法。通过Monte Carlo模拟,证明了所提出几乎无偏岭估计和最优几乎无偏岭参数的优良性。

For the complex collinearity of the Gamma regression model,this paper proposes the almost unbiased ridge estimation of the Gamma regression model.The paper first studies the linear relationship between almost unbiased ridge estimation and maximum likelihood estimation,proving that almost unbiased ridge estimation is a compression estimate.Then,under the criterion of mean square error,the paper discusses the functional properties of the mean square error of almost unbiased ridge estimation with respect to parameter[K],presenting the existence theorem that almost unbiased ridge estimation is superior to maximum likelihood estimation and ordinary ridge estimation.Finally,the paper discusses a method to determine the optimal almost unbiased ridge parameters.And Monte Carlo simulation method is used to verify the superiority of the proposed almost unbiased ridge estimation and the optimal almost unbiased ridge parameter.