Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp estimation in sup norm with random design   The aim of this paper is to recover the regression function with sup norm
loss. We construct an asymptotically sharp estimator which converges with the
spatially dependent rate r\_{n, \mu}(x) = P \big(\log n / (n \mu(x)) \big)^{s /
(2s + 1)}, where $\mu$ is the design density, $s$ the regression smoothness,
$n$ the sample size and $P$ is a constant expressed in terms of a solution to a
problem of optimal recovery as in Donoho (1994). We prove this result under the
assumption that $\mu$ is positive and continuous. This estimator combines
kernel and local polynomial methods, where the kernel is given by optimal
recovery, which allows to prove the result up to the constants for any $s > 0$.
Moreover, the estimator does not depend on $\mu$. We prove that $r\_{n,
\mu}(x)$ is optimal in a sense which is stronger than the classical minimax
lower bound. Then, an inhomogeneous confidence band is proposed. This band has
a non constant length which depends on the local amount of data.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph