Near-optimal mean estimators with respect to general norms
Near-optimal mean estimators with respect to general norms
复制标题
相对于一般规范的近最优均值估计量
DOI：
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发表时间：
2018
影响因子：
2
通讯作者：
S. Mendelson
中科院分区：
文献类型：
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作者：
G. Lugosi;S. Mendelson
我们研究基于 i.i.d 估计 $$\mathbb {R}^d$$Rd 中随机向量均值的问题。样本，当估计器的准确性通过 $$\mathbb {R}^d$$Rd 上的一般范数来测量时。我们构造一个估计器（取决于范数），在随机向量具有明确定义的协方差矩阵的唯一假设下，该估计器可以实现本质上最优的精度/置信度权衡。争论的核心是在一类实值函数中构建统一的均值估计器。
We study the problem of estimating the mean of a random vector in $$\mathbb {R}^d$$Rd based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on $$\mathbb {R}^d$$Rd. We construct an estimator (that depends on the norm) that achieves an essentially optimal accuracy/confidence tradeoff under the only assumption that the random vector has a well-defined covariance matrix. At the heart of the argument is the construction of a uniform median-of-means estimator in a class of real valued functions.