Many variables encountered in practice have skewed distributions. While the sample mean is unbiased for the true mean regardless of the underlying distribution that generated the sample observations, it can be highly unstable in the context of skewed distributions. To cope with this problem, we propose an efficient estimator of the population mean based on the concept of conditional bias of a unit, which can be viewed as a measure of its influence. The idea is to reduce the impact of the sample units that have a large influence. The resulting estimator depends on a cut-off value. We suggest selecting the cut-off value that minimizes the maximum absolute estimated conditional bias with respect to the proposed estimator. An estimator of the mean square error is also presented. An empirical investigation comparing several estimators in terms of relative bias and relative efficiency suggests that the proposed estimator and the estimator of its mean square error perform well for a wide class of distributions.

中文翻译：

---

偏态分布的有效非参数估计

实践中遇到的许多变量都有偏态分布。尽管样本均值对于真实均值是无偏的，而不管生成样本观测值的基础分布如何，但在偏态分布的情况下它可能非常不稳定。为了解决这个问题，我们提出了一种基于单元条件偏差概念的总体均值的有效估计器，可以将其视为对其影响的度量。其想法是减少具有较大影响的样本单元的影响。结果估计量取决于截止值。我们建议选择一个临界值，以使相对于所提出的估算器的最大绝对估算条件偏差最小。还提供了均方误差的估计值。