On mean estimation for heteroscedastic random variables

Open Access
  • Authors: Gábor Lugosi.
  • Statistics
  • Annales de l'institut Henri Poincare (B) Probability and Statistics
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We study the problem of estimating the common mean μ of n independent symmetric random variables with different and unknown standard deviations σ1≤σ2≤⋯≤σn. We show that, under some mild regularity assumptions on the distribution, there is an adaptive estimator ˆμ such that it is invariant to permutations of the elements of the sample and satisfies that, up to logarithmic factors, with high probability,

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