Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stein's method for products of normal random variables and zero bias
  couplings   In this paper we extend Stein's method to the distribution of the product of
$n$ independent mean zero normal random variables. A Stein equation is obtained
for this class of distributions, which reduces to the classical normal Stein
equation in the case $n=1$. This Stein equation motivates a generalisation of
the zero bias transformation. We establish properties of this new
transformation, and illustrate how they may be used together with the Stein
equation to assess distributional distances for statistics that are
asymptotically distributed as the product of independent central normal random
variables. We end by proving some product normal approximation theorems.

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The categories of this paper are: cond-mat
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The categories of this paper are: stat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
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The categories of this paper are: physics