We consider the geometric quantile and various definitions of the component-wise quantile in infinite dimensions and show their existence, uniqueness and continuity. Building on these results, we introduce and study the properties of the Quantile-of-Estimates (QoE) estimator, a robustification procedure for a large class of estimators. For example, given an estimator that is asymptotically normal, the QoE estimator is asymptotically normal even in the presence of contaminated data.
翻译:我们从无限的维度考虑成份量的几何量化和各种定义,并表明其存在、独特性和连续性。我们以这些结果为基础,介绍和研究估计量量(QoE)估测器的特性,这是对一大批估测器的一种稳健化程序。例如,鉴于一个估算值是正常的,即使存在受污染的数据,量化估测器也是正常的。