Near-optimal mean estimators with respect to general norms
成果类型：
Article
署名作者：
Lugosi, Gabor; Mendelson, Shahar
署名单位：
Pompeu Fabra University; ICREA; Universite Paris Cite; Sorbonne Universite; Australian National University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-019-00906-4
发表日期：
2019
页码：
957-973
关键词：
摘要：
We study the problem of estimating the mean of a random vector in based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on . 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.