论文标题
通用鲁棒性程序
A universal robustification procedure
论文作者
论文摘要
我们开发了一个程序，该程序将任何渐近正常的估计器转化为渐近正常估计器，该估计量其分布对任意数据污染具有鲁棒性。更普遍地，我们的过程将渐近分布在原点上具有正和连续密度的估计量转换为渐近正常估计量，其分布对任意污染是可靠的。在制定这样的过程中，我们证明了有限和无限维度中综合和几何分位数的新一般特性。
We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose asymptotic distribution has positive and continuous density at the origin into an asymptotically normal estimator whose distribution is robust to arbitrary contamination. In developing such a procedure we prove new general properties of componentwise and geometric quantiles in both finite and infinite dimensions.
