We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriately weighting the score function at each observation in the maximum likelihood score equation. The weight function determines the compatibility of each observation with the model in relation to the remaining observations and applies a downweighting only if it is necessary, rather than automatically downweighting a proportion of the observations all the time. This allows the estimators to retain full asymptotic efficiency at the model. We establish all the theoretical properties of the proposed estimators and substantiate the theory developed through simulation and real data examples. Our approach provides an alternative to the weighted likelihood method of Markatou et al. (J Stat Plan Inference 57(2):215–232, 1997; J Am Stat Assoc 93(442):740–750, 1998).

中文翻译：

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基于新加权似然法的统计推断

我们讨论了一种用于稳健参数估计的新加权似然方法。该方法的动机是需要生成一个简单的估计策略，该策略提供一个强大的解决方案，当正确指定模型时，该解决方案同时完全有效。这是通过在最大似然得分方程中对每个观察值的得分函数进行适当加权来实现的。权重函数确定每个观测值与模型相对于剩余观测值的兼容性，并仅在必要时应用减重，而不是始终自动减重一部分观测值。这允许估计器在模型上保持完全渐近效率。我们建立了所提出的估计器的所有理论属性，并证实了通过模拟和真实数据示例开发的理论。我们的方法为 Markatou 等人的加权似然方法提供了一种替代方法。（J Stat Plan Inference 57(2):215–232, 1997；J Am Stat Assoc 93(442):740–750, 1998）。