Covering numbers, Vapnik–Červonenkis classes and bounds for the star-discrepancy

doi:10.1016/j.jco.2004.01.001

Journal of Complexity

Volume 20, Issue 4, August 2004, Pages 477-483

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Abstract

We show new lower bounds for the star-discrepancy and its inverse for subsets of the unit cube. They are polynomial in the quotient d/n of the number n of sample points and the dimension d. They provide the best-known lower bounds for n not too large compared with d.

Keywords

Discrepancy

Vapnik-

C ̌

ervonenkis classes

Covering numbers

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¹: Research of the author is supported by the DFG Emmy-Noether Grant Hi 584/2-3