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Dominated concentration

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  • Maurer, Andreas

Abstract

The concentration properties of one random variable may be governed by the values of another random variable which is concentrated and more easily analyzed. We present a general concentration inequality to handle such cases and apply it to the eigenvalues of the Gram matrix for a sample of independent vectors distributed in the unit ball of a Hilbert space. For large samples the deviation of the eigenvalues from their mean is shown to scale with the largest eigenvalue.

Suggested Citation

  • Maurer, Andreas, 2010. "Dominated concentration," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 683-689, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:683-689
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