Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation by log-concave distributions, with applications to
  regression   We study the approximation of arbitrary distributions $P$ on $d$-dimensional
space by distributions with log-concave density. Approximation means minimizing
a Kullback--Leibler-type functional. We show that such an approximation exists
if and only if $P$ has finite first moments and is not supported by some
hyperplane. Furthermore we show that this approximation depends continuously on
$P$ with respect to Mallows distance $D_1(\cdot,\cdot)$. This result implies
consistency of the maximum likelihood estimator of a log-concave density under
fairly general conditions. It also allows us to prove existence and consistency
of estimators in regression models with a response $Y=\mu(X)+\epsilon$, where
$X$ and $\epsilon$ are independent, $\mu(\cdot)$ belongs to a certain class of
regression functions while $\epsilon$ is a random error with log-concave
density and mean zero.

32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat