Multivariate mean estimation with direction-dependent accuracy

  • Gábor Lugosi

    Pompeu Fabra University, Barcelona; ICREA, Barcelona; Barcelona School of Economics, Spain
  • Shahar Mendelson

    University of Warwick, Coventry, UK; Australian National University, Canberra, Australia
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Abstract

We consider the problem of estimating the mean of a random vector based on independent, identically distributed observations.We prove the existence of an estimator that has a nearoptimal error in all directions in which the variance of the one-dimensional marginal of the random vector is not too small: with probability , the procedure returns which satisfies, for every direction , where and is a constant. To achieve this, we require only slightly more than the existence of the covariance matrix, in the form of a certain moment-equivalence assumption.

Cite this article

Gábor Lugosi, Shahar Mendelson, Multivariate mean estimation with direction-dependent accuracy. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1321