Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Negative Dependence Properties of Latin Hypercube Samples and
  Scrambled Nets   We study the notion of $\gamma$-negative dependence of random variables. This
notion is a relaxation of the notion of negative orthant dependence (which
corresponds to $1$-negative dependence), but nevertheless it still ensures
concentration of measure and allows to use large deviation bounds of
Chernoff-Hoeffding- or Bernstein-type. We study random variables based on
random points $P$. These random variables appear naturally in the analysis of
the discrepancy of $P$ or, equivalently, of a suitable worst-case integration
error of the quasi-Monte Carlo cubature that uses the points in $P$ as
integration nodes. We introduce the correlation number, which is the smallest
possible value of $\gamma$ that ensures $\gamma$-negative dependence. We prove
that the random variables of interest based on Latin hypercube sampling or on
$(t,m,d)$-nets do, in general, not have a correlation number of $1$, i.e., they
are not negative orthant dependent. But it is known that the random variables
based on Latin hypercube sampling in dimension $d$ are actually
$\gamma$-negatively dependent with $\gamma \le e^d$, and the resulting
probabilistic discrepancy bounds do only mildly depend on the $\gamma$-value.

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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph