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 disturbi...