论文标题
强大而有效的平均估计：一种基于自分量总和的特性的方法
Robust and efficient mean estimation: an approach based on the properties of self-normalized sums
论文作者
论文摘要
令$ x $为一个随机变量，均值和有限差异。我们提供了一个新的估计器，即$ x $的平均值，相对于样本中异常值的可能存在，可提供紧密的下毛口偏差保证，而没有对分布的形状或尾巴进行任何其他假设，而且渐近效率高。这是第一个将所有这些品质结合在一个包装中的估计器。我们的构建灵感来自自相应的总和所具有的鲁棒性特性。与先前已知的技术相比，理论发现补充了数值模拟，强调了所提出的估计量的强劲性能。
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and moreover is asymptotically efficient. This is the first estimator that provably combines all these qualities in one package. Our construction is inspired by robustness properties possessed by the self-normalized sums. Theoretical findings are supplemented by numerical simulations highlighting strong performance of the proposed estimator in comparison with previously known techniques.
