Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A theory of nonparametric regression in the presence of complex nuisance
  components   In this paper, we consider the nonparametric random regression model
$Y=f_1(X_1)+f_2(X_2)+\epsilon$ and address the problem of estimating the
function $f_1$. The term $f_2(X_2)$ is regarded as a nuisance term which can be
considerably more complex than $f_1(X_1)$. Under minimal assumptions, we prove
several nonasymptotic $L^2(\mathbb{P}^X)$-risk bounds for our estimators of
$f_1$. Our approach is geometric and based on considerations in Hilbert spaces.
It shows that the performance of our estimators is closely related to geometric
quantities, such as minimal angles and Hilbert-Schmidt norms. Our results
establish new conditions under which the estimators of $f_1$ have up to first
order the same sharp upper bound as the corresponding estimators of $f_1$ in
the model $Y=f_1(X_1)+\epsilon$. As an example we apply the results to an
additive model in which the number of components is very large or in which the
nuisance components are considerably less smooth than $f_1$. In particular, the
results apply to an asymptotic scenario in which the number of components is
allowed to increase with the sample size.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol