A reference for a Gaussian inequality ($\mathbb{E} \max_i X_i$)

I eventally found these two references:

  • from [1]: the expected value of the maximum of $N$ independent standard Gaussians: Theorem 2.5 and Exercise 2.17, p. 49; for a concentration result, combined with the variance (which is $O(1)$). Exercise 3.24 (or Theorem 5.8 for directly a concentration inequality).
  • from [2], Theorem 3.12

[1] Concentration Inequalities: A Nonasymptotic Theory of Independence By Stéphane Boucheron, Gábor Lugosi, Pascal Massart (2013)

[2] Concentration Inequalities and Model Selection, by Pascal Massart (2003)


You have an explicit asymptotic result concerning the limit distribution in this post and the associated references.

Tags:

Normal Distribution

Probability Theory

Probability Distributions

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