奇异线性模型下最小范数二次无偏估计关于误差分布的稳健性

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance in Terms of Error Distributions under the Singular Linear Model

讨论奇异线性模型下方差σ2的最小范数二次无偏估计关于误差分布的稳健性问题,得到方差的最小范数二次无偏估计保持最优的误差项的最大分布类.进一步考虑可估计函数Xβ的最佳线性无偏估计的稳健性,得到了Xβ的最佳线性无偏估计与方差σ2的最小范数二次无偏估计同时最优的误差项的最大类.

Robustness of the minimum norm quadratic unbiased estimator of variance in terms of error distributions is discussed in singular linear model.We explore the maximal distribution class of error term,where the minimum norm quadratic unbiased estimator of variance σ2 holds its optimality.Furthermore considering robustness of the best linear unbiased estimator of estimable function Xβ,we obtain the maximal distribution class of error term,where the minimum norm quadratic unbiased estimator of variance σ2 and the best linear unbiased estimator of Xβ keep optimality simultaneously.