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单词 Bernstein inequality
释义
Bernstein inequality

Statistics
  • A stronger version of the Chebyshev inequality. Let X1, X2,…, Xn be independent random variables, such that, for j=1, 2,…, n, Xj has expected value 0 and | Xj |≤M. Bernstein showed, in a 1926 paper, that, for all positive ε,Bernstein inequalitywhere Var(Xj) = σj2. See also Chebyshev inequality; Hölder inequality; Kolmogorov inequality; Markov inequality; Minkowski inequality.


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