Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical inference for a partially observed interacting system of
  Hawkes processes   We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$
for some large $K<N$. We model the relationships of individuals by i.i.d.
Bernoulli($p$)-random variables, where $p\in (0,1]$ is an unknown parameter.
The rate of action of each individual depends on some unknown parameter $\mu>
0$ and on the sum of some function $\phi$ of the ages of the actions of the
individuals which influence him. The function $\phi$ is unknown but we assume
it rapidly decays. The aim of this paper is to estimate the parameter $p$
asymptotically as $N\to \infty$, $K\to \infty$, and $t\to \infty$. Let $m_t$ be
the average number of actions per individual up to time $t$. In the subcritical
case, where $m_t$ increases linearly, we build an estimator of $p$ with the
rate of convergence
$\frac{1}{\sqrt{K}}+\frac{N}{m_t\sqrt{K}}+\frac{N}{K\sqrt{m_t}}$. In the
supercritical case, where $m_{t}$ increases exponentially fast, we build an
estimator of $p$ with the rate of convergence
$\frac{1}{\sqrt{K}}+\frac{N}{m_{t}\sqrt{K}}$.

24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys