Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonparametric intensity estimation from noisy observations of a Poisson
  process under unknown error distribution   We consider the nonparametric estimation of the intensity function of a
Poisson point process in a circular model from indirect observations
$N_1,\ldots,N_n$. These observations emerge from hidden point process
realizations with the target intensity through contamination with additive
error. In case that the error distribution can only be estimated from an
additional sample $Y_1,\ldots,Y_m$ we derive minimax rates of convergence with
respect to the sample sizes $n$ and $m$ under abstract smoothness conditions
and propose an orthonormal series estimator which attains the optimal rate of
convergence. The performance of the estimator depends on the correct
specification of a dimension parameter whose optimal choice relies on
smoothness characteristics of both the intensity and the error density. We
propose a data-driven choice of the dimension parameter based on model
selection and show that the adaptive estimator attains the minimax optimal
rate.

14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex