---
res:
bibo_abstract:
- 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated
for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure
and placing a random point inside each of the N=md cubes. We prove that, for N
sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where
the upper bound with an unspecified constant Cd was proven earlier by Beck. Our
proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and
a suitably taylored Bernstein inequality; we have reasons to believe that the
upper bound has the sharp scaling in N. Additional heuristics suggest that jittered
sampling should be able to improve known bounds on the inverse of the star-discrepancy
in the regime N≳dd. We also prove a partition principle showing that every partition
of [0,1]d combined with a jittered sampling construction gives rise to a set whose
expected squared L2-discrepancy is smaller than that of purely random points.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Florian
foaf_name: Pausinger, Florian
foaf_surname: Pausinger
foaf_workInfoHomepage: http://www.librecat.org/personId=2A77D7A2-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Steinerberger, Stefan
foaf_surname: Steinerberger
bibo_doi: 10.1016/j.jco.2015.11.003
bibo_volume: 33
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Academic Press@
dct_title: On the discrepancy of jittered sampling@
...