Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence analysis of quasi-Monte Carlo sampling for quantile and
  expected shortfall   Quantiles and expected shortfalls are usually used to measure risks of
stochastic systems, which are often estimated by Monte Carlo methods. This
paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence
rate is asymptotically better than Monte Carlo in the numerical integration. We
first prove the convergence of QMC-based quantile estimates under very mild
conditions, and then establish a deterministic error bound of $O(N^{-1/d})$ for
the quantile estimates, where $d$ is the dimension of the QMC point sets used
in the simulation and $N$ is the sample size. Under certain conditions, we show
that the mean squared error (MSE) of the randomized QMC estimate for expected
shortfall is $o(N^{-1})$. Moreover, under stronger conditions the MSE can be
improved to $O(N^{-1-1/(2d-1)+\epsilon})$ for arbitrarily small $\epsilon>0$.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th