We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting, where each bit depends only on a single sample, and the second is a partial quantization setting, in which the estimator may use a small fraction of unquantized data.

翻译：本文研究了在量化和对抗性污染条件下的均值估计问题。我们构建了多变量鲁棒估计器，在两种不同设置下均达到对数因子级别的最优性。第一种是单比特设置，其中每个比特仅依赖于单个样本；第二种是部分量化设置，其中估计器可以使用少量未量化数据。