Covering numbers, vapnik-červonenkis classes and bounds for the star-discrepancy

Authors:
Aicke Hinrichs
Affiliations:
Department of Mathematics, Faculty of Mathematics and Computer Science, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 2, Jena D-07743, Germany
Venue:
Journal of Complexity
Year:
2004

Citing 3
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Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension

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Some open problems concerning the star-discrepancy

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Note: A note on the existence of sequences with small star discrepancy

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The randomized complexity of indefinite integration

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Asymptotic behavior of average Lp -discrepancies

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A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting

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On the inverse of the discrepancy for infinite dimensional infinite sequences

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A lower bound for the discrepancy of a random point set

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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.