Bounds for the Uniform Deviation of Empirical Measures

@inproceedings{Luc1982BoundsFT,
  title={Bounds for the Uniform Deviation of Empirical Measures},
  author={Luc and DEVROYE},
  year={1982}
}
  • Luc, DEVROYE
  • Published 1982
If x, )...) X, are independent identically distributed Rd-valued random vectors with probability measure p and empirical probability measure p,, and if QZ is a subset of the Bore1 sets on Rd, then we show that P{sup,,~ IF,@) -,u(A)( > E) < cs(Q, n*) eCZnr2, where c is an explicitly given constant, and s(W, n) is the maximum over all (x, ,..., XJ E Rd” of the number of different sets in {lx , ,..., x.} nA 1 A E a). The bound strengthens a result due to Vapnik and Chervonenkis. 

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