A weighted maximum likelihood method (WMLM) of robust estimation of experimental data with outliers is proposed in this work. The method allows effective robust asymptotically unbiased estimates to be obtained under conditions of aprioristic uncertainty. Based on the WMLM, adaptive robust algorithms have been synthesized for solving semiparametric and semi-nonparametric problems of heterogeneous data processing. It is shown that for heterogeneous data samples, these estimates converge to the maximum likelihood estimates for each distribution from the Tukey supermodel not only in the presence of major, but also minor asymmetric and symmetric outliers.

在这项工作中提出了一种对具有异常值的实验数据进行稳健估计的加权最大似然法（WMLM）。该方法允许在先验不确定性的条件下获得有效的稳健渐近无偏估计。在WMLM的基础上，综合了自适应鲁棒算法来解决异构数据处理的半参数和半非参数问题。结果表明，对于异构数据样本，这些估计不仅在存在主要的，而且存在次要的不对称和对称异常值的情况下，都收敛到 Tukey 超模型中每个分布的最大似然估计。