自适应临界值的等价权函数及抗差估计方法

Equivalent weight function and robust estimation method with adaptive criterion

抗差估计中的等价权函数通常由正态分布统计量或学生分布统计量构造,其临界值一般根据经验直接设定,由此将带来参数估计效率以及抗差性方面的风险.为了削弱该风险,在IGGⅢ方案的基础上,提出了一种自适应临界值的等价权函数.利用中位数残差计算出一定置信水平下的残差置信区间,以该区间的边界构造出新的等价权函数临界值,该临界值不再根据经验直接确定.并研究了基于该等价权函数的抗差参数估计方法,通过模拟试验与实际算例验证了该方法的有效性.结果表明:自适应临界值的等价权抗差估计方法比人为直接设定临界值的等价权方法抗差性更强,可靠性更高.

The equivalent weight function of the robust estimation is usually established by statistics of normal distribution or t distribution, and the critical values are often fixed by experience which brings the risks of the parameter estimation efficiency and the robustness. Based on the IGGI]I scheme, a new equivalent weight function with adaptive criterion was proposed to resist the risks. The residual confidence interval was computed with the median residuals, and the critical values of the novel equivalent weight function were constructed using the boundaries of the interval. In this new function, the critical values were not directly determined by experience, and the equivalent weight robust estimation method based on the presented function was investigated, then the validity of the proposed method was demonstrated with simulations and experiments. The results show that the new method is much more robust and reliable than the equivalent weight robust estimation method where the critical values are determined artificially.