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.

翻译：我们开发了一种程序,将任何无症状正常的测算器转换成一个无症状正常的测算器,该测算器的分布对任意的数据污染十分可靠。 更一般地说,我们的程序将任何无症状分布在源头具有正和连续密度的测算器转换成一个无症状正常的测算器,该测算器的分布对任意污染非常有力。 在开发这样一个程序时,我们证明在有限的和无限的维度中,组件和几何定量都具有新的一般特性。