Near-optimal mean estimators with respect to general norms

Gábor Lugosi*, Shahar Mendelson

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)957-973
    Number of pages17
    JournalProbability Theory and Related Fields
    Volume175
    Issue number3-4
    DOIs
    Publication statusPublished - 1 Dec 2019

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