约束条件下线性模型协方差阵扰动的影响分析

Influence Analysis of Covariance Matrix Disturbance in Linear Model with Respect to a Restricted Condition

该文研究了协方差阵扰动和数据删除对最佳线性无偏估计(BLUE)的影响问题,给出了在约束条件下一般线性模型与在约束条件下Gauss-Markov模型及在约束条件下数据删除模型中回归参数β的BLUE之间的关系式．作者还定义了度量影响大小的广义Cook距离D_v,并给出了D_v的两个计算公式．

In this paper, the authors study the issue of the influence of Best Linear Unbiased Estimate （BLUE） with covariance matrix disturbing or data missing. The relationship of the BLUE of regression parameter β among some linear models with respect to restricted condition Lβ = 0, such as Gauss-Markov model, generalized linear model and linear model with delected data, is made explicitly. In addition, the authors also propose the generalized Cook distance Dv to asses the disturbing influence, and obtain two computational formulae of Dv.