Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the chi-square approximation of Friedman's statistic by
  Stein's method   Friedman's chi-square test is a non-parametric statistical test for $r\geq2$
treatments across $n\ge1$ trials to assess the null hypothesis that there is no
treatment effect. We use Stein's method with an exchangeable pair coupling to
derive an explicit bound on the distance between the distribution of Friedman's
statistic and its limiting chi-square distribution, measured using smooth test
functions. Our bound is of the optimal order $n^{-1}$, and also has an optimal
dependence on the parameter $r$, in that the bound tends to zero if and only if
$r/n\rightarrow0$. From this bound, we deduce a Kolmogorov distance bound that
decays to zero under the weaker condition $r^{1/2}/n\rightarrow0$.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys