粗差数学期望平移模型的理论研究

现有文献对数学期望平移模型的理论分析仅考虑了观测值统计独立的特殊情况。基于观测值统计相关的一般情况，导出了数学期望平移参数估值（Ｓｉ）的简明表达式。在此基础上，采用统计预测理论对Ｓｉ进行了直观的理论解释，扩展了统计学文献中的有关结论。借助于实例，分析了Ｓｉ与最小二乘残差的本质区别。

A Research on the Mean Shift Outlier Models

Based on the mean shift outlier model,outliers are considered as the mean shift parameters of the corresponding observations, which can be estimated by using the least squares method.In literature,the estimation of the mean shift parameters is often formulated as the complicated linear function of the least squares residuals biased by the presence of outliers,and its statistical performance is not lucid. In this paper,the estimated mean shift parameters have been further derived and represented as a concise formula in the general case of correlated observations,from which the estimated mean shift parameters are interpreted with the concept of statistical prediction. Finally,the essential distinction between the estimated mean shift parameters and residuals is demonstrated by a practical example.