线性回归的几乎无偏两参数岭M估计

On almost unbiased two-parameter ridge-type M-estimatorfor linear regression model

针对线性回归模型中设计矩阵存在复共线性问题,利用几乎无偏估计和两参数岭估计的思想,提出了几乎无偏两参数岭M估计。在均方误差准则下,得到了几乎无偏两参数岭M估计优于两参数岭M估计、几乎无偏两参数岭估计,并通过数值模拟验证了估计方法和结论的有效性。

Considering the existence of multicollinearity in the design matrix of the linear model,this paper proposed a new ridge-type M-estimatorfor almost unbiased two-parameter based on almost unbiased estimation and two parameter ridge-type M-estimator.Under the mean square errorcriterion,the proposed estimator outperforms two-parameter ridge M-estimator and the almost unbiased two-parameter ridge estimate.Moreover,a numerical example experiment was presented to verify the validity of the estimation method and conclusions.