Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the empirical multilinear copula process for count data   Continuation refers to the operation by which the cumulative distribution
function of a discontinuous random vector is made continuous through
multilinear interpolation. The copula that results from the application of this
technique to the classical empirical copula is either called the multilinear or
the checkerboard copula. As shown by Genest and Ne\v{s}lehov\'{a} (Astin Bull.
37 (2007) 475-515) and Ne\v{s}lehov\'{a} (J. Multivariate Anal. 98 (2007)
544-567), this copula plays a central role in characterizing dependence
concepts in discrete random vectors. In this paper, the authors establish the
asymptotic behavior of the empirical process associated with the multilinear
copula based on $d$-variate count data. This empirical process does not
generally converge in law on the space $\mathcal {C}([0,1]^d)$ of continuous
functions on $[0,1]^d$, equipped with the uniform norm. However, the authors
show that the process converges in $\mathcal{C}(K)$ for any compact
$K\subset\mathcal{O}$, where $\mathcal{O}$ is a dense open subset of $[0,1]^d$,
whose complement is the Cartesian product of the ranges of the marginal
distribution functions. This result is sufficient to deduce the weak limit of
many functionals of the process, including classical statistics for monotone
trend. It also leads to a powerful and consistent test of independence which is
applicable even to sparse contingency tables whose dimension is sample size
dependent.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an