一般线性模型下方差最小范数二次无偏估计的稳健性(英文)

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

中文关键词:  一般线性模型  广义逆  正交投影  最小范数二次无偏估计

英文关键词:general linear model  generalized inverse  orthogonal projector  minimum norm quadratic unbiased estimator

中文摘要:

      本文给出了一般线性模型下,由最小二乘得到的方差估计与最小范数二次无偏估计相等的充分必要条件,并且当Gauss-Markov估计与最小二乘估计相等时,可以得到一个简单的等价条件。

英文摘要:

      In this paper, necessary and sufficient conditions for equalities between α²y¹(I-P_X)y and σ² under the general linear model, where and α² is a known positive number, are derived. Furthermore, when the Gauss-Markov estimators and the ordinary least squares estimators are identical, we obtain a simple equivalent condition.