TY - JOUR
T1 - Near-optimal mean estimators with respect to general norms
AU - Lugosi, Gábor
AU - Mendelson, Shahar
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We study the problem of estimating the mean of a random vector in Rd based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on 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.
AB - We study the problem of estimating the mean of a random vector in Rd based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on 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.
UR - http://www.scopus.com/inward/record.url?scp=85064086341&partnerID=8YFLogxK
U2 - 10.1007/s00440-019-00906-4
DO - 10.1007/s00440-019-00906-4
M3 - Article
SN - 0178-8051
VL - 175
SP - 957
EP - 973
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -