粗差验后方差的无偏估计与最优稳健估计

The Unbiased Estimation of Posterior Variance of Gross Error and the Optimal Robust Estimate

在正态粗差假设下导出了粗差验后方差的无偏估计 ,对误差方差膨胀模型和误差均值移动模型 ,两者的无偏估计公式是相同的。这证明了李德仁验后方差和朱建军方差不是无偏的。由无偏方差定义的彭方法是正态粗差假设下的最优稳健估计。

Under the normal assumption of gross errors, this paper derives the unbiased estimate formula of the posterior variance of the gross errors. For stochastic error model and mean shift error model, they have the same estimate formula. This proves that Li Deren posterior variance and Zhu Jianjun posterior variance aren't unbiased. The corresponding Peng method whose weight is detemined from the unbiased posterior variance is the most efficient robust estimate.