Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Risk aggregation with empirical margins: Latin hypercubes, empirical
  copulas, and convergence of sum distributions   This paper studies convergence properties of multivariate distributions
constructed by endowing empirical margins with a copula. This setting includes
Latin Hypercube Sampling with dependence, also known as the Iman--Conover
method. The primary question addressed here is the convergence of the component
sum, which is relevant to risk aggregation in insurance and finance.
  This paper shows that a CLT for the aggregated risk distribution is not
available, so that the underlying mathematical problem goes beyond classic
functional CLTs for empirical copulas. This issue is relevant to Monte-Carlo
based risk aggregation in all multivariate models generated by plugging
empirical margins into a copula.
  Instead of a functional CLT, this paper establishes strong uniform
consistency of the estimated sum distribution function and provides a
sufficient criterion for the convergence rate $O(n^{-1/2})$ in probability.
These convergence results hold for all copulas with bounded densities. Examples
with unbounded densities include bivariate Clayton and Gauss copulas. The
convergence results are not specific to the component sum and hold also for any
other componentwise non-decreasing aggregation function. On the other hand,
convergence of estimates for the joint distribution is much easier to prove,
including CLTs.
  Beyond Iman--Conover estimates, the results of this paper apply to
multivariate distributions obtained by plugging empirical margins into an exact
copula or by plugging exact margins into an empirical copula.

0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom