临界值可变的抗差估计等价权函数

抗差估计等价权函数一般由正态分布统计量构造,其临界值(或称准则)一般由实际经验确定.首先分析了正态分布统计量和学生化残差统计量的区别,然后分别讨论了基于这两种统计量构造的等价权函数的区别.研究表明,利用学生化残差统计量构造的等价权函数以及顾及误差显著性水平确定的临界值,不仅考虑了观测误差的大小,而且还可以顾及了实际观测的图形强度和多余观测数,可以克服人为确定临界值可能带来的参数估计的有效性和抗差性方面的风险.

Modified Equivalent Weight Function with Variable Criterion for Robust Estimation

The equivalent weight function in robust estimation is usually constructed by the statistics of normal distribution. The critical values are often fixed by experience. In this article, the differences between the statistics of normal distribution and the statistics of t distribution are analyzed. Then the differences between the equivalent weight functions based on the two statistics are discussed. It is demonstrated that the equivalent weight function constructed by t distribution with its critical values determined by the significance level which has relations with observation errors, the design matrix of observations and redundant observation number, can resist the risk of the parameter estimation efficiency and robustness resulted from the constant critical values.