As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that their maximum biases concerning the mean can be quite different, but the underlying mechanisms largely remain unclear. This study exploited a semiparametric method to classify distributions by the asymptotic orderliness of quantile combinations with varying breakdown points, showing their interrelations and connections to parametric distributions. Further deductions explain why the Winsorized mean typically has smaller biases compared to the trimmed mean; two sequences of semiparametric robust mean estimators emerge, particularly highlighting the superiority of the median Hodges Lehmann mean. This article sheds light on the understanding of the common nature of probability distributions.

翻译：作为统计学中最基础的问题，稳健位置估计已有诸多卓越解决方案，如截尾均值、Winsorized均值、Hodges-Lehmann估计量、Huber M估计量以及均值中位数。近期研究表明，这些估计量相对于均值的最大偏差可能存在显著差异，但其潜在机制仍不明确。本研究采用半参数方法，依据不同崩溃点下分位数组合的渐近有序性对分布进行分类，揭示其相互关系及与参数分布的联系。进一步推导解释了为何Winsorized均值通常比截尾均值具有更小的偏差；由此衍生出两个半参数稳健均值估计量序列，尤其凸显了中位数Hodges-Lehmann均值的优越性。本文为理解概率分布的共性规律提供了新见解。