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• W3200626344 abstract "We introduce a class of $gamma$-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a $gamma$-negatively dependent $N$-point sample in dimension $d$ we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on $N$, $d$, and $gamma$. These bounds generalize the probabilistic bounds for Monte Carlo samples from [Heinrich et al., Acta Arith. 96 (2001), 279--302] and [C.~Aistleitner, J.~Complexity 27 (2011), 531--540], and they are optimal for Monte Carlo and Latin hypercube samples. In the special case of Monte Carlo samples the constants that appear in our bounds improve substantially on the constants presented in the latter paper and in [C.~Aistleitner, M.~T.~Hofer, Math. Comp.~83 (2014), 1373--1381]." @default.
• W3200626344 created "2021-09-27" @default.
• W3200626344 creator A5027293444 @default.
• W3200626344 creator A5063331845 @default.
• W3200626344 date "2021-08-01" @default.
• W3200626344 modified "2023-09-29" @default.
• W3200626344 title "Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples" @default.
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• W3200626344 doi "https://doi.org/10.1214/20-aap1638" @default.
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