Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical inference for time-changed L\'{e}vy processes via composite
  characteristic function estimation   In this article, the problem of semi-parametric inference on the parameters
of a multidimensional L\'{e}vy process $L_t$ with independent components based
on the low-frequency observations of the corresponding time-changed L\'{e}vy
process $L_{\mathcal{T}(t)}$, where $\mathcal{T}$ is a nonnegative,
nondecreasing real-valued process independent of $L_t$, is studied. We show
that this problem is closely related to the problem of composite function
estimation that has recently gotten much attention in statistical literature.
Under suitable identifiability conditions, we propose a consistent estimate for
the L\'{e}vy density of $L_t$ and derive the uniform as well as the pointwise
convergence rates of the estimate proposed. Moreover, we prove that the rates
obtained are optimal in a minimax sense over suitable classes of time-changed
L\'{e}vy models. Finally, we present a simulation study showing the performance
of our estimation algorithm in the case of time-changed Normal Inverse Gaussian
(NIG) L\'{e}vy processes.

20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th