多种权函数固定临界值与可变临界值抗差估计的比较

抗差估计等价权函数中临界值一般定为常数。若基于学生化分布构造标准化残差,其临界值可由观测自由度以及给定的显著性水平确定。首先对几种权函数进行了分析和比较,然后讨论了各个权函数抗差性与误差显著性水平以及由之确定的临界值的关系。利用模拟数据详细分析和比较了不同的权函数在不同显著性水平下的抗差性,针对不同的权函数给出了合适的显著性水平；并将其与经验确定的常数临界值所对应的抗差估计进行比较,发现这种基于合适的显著性水平下的权函数不仅具有较严格的理论基础,而且计算也是行之有效的。

Comparison of robustness between equivalent weight functions with constant critical values and variable critical values

Critical values of the equivalent weight function are often fixed in constants in robust estimation.If the standard residuals are constructed by the statistic of t distribution,the critical values are variable which depends on the degree of observation freedom and the given significance levels.Different equivalent weight functions are compared and analyzed.Then the relations between the robustness and the significance levels are analyzed.The robustness of different equivalent weight functions based on different significance levels with the constant critical values and variable values is analyzed and compared by simulated data.It is demonstrated that the robustness and efficiency of parameter estimates could be improved by the equivalent weight functions with suitable significance levels.