Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal rate of convergence for nonparametric change-point estimators
  for nonstationary sequences   Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that
$\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if
$i>n\theta$, where $0<\theta <1$ is the location of the change-point to be
estimated. We construct a class of estimators based on the empirical measures
and a seminorm on the space of measures defined through a family of functions
$\mathcal{F}$. We prove the consistency of the estimator and give rates of
convergence under very general conditions. In particular, the $1/n$ rate is
achieved for a wide class of processes including long-range dependent sequences
and even nonstationary ones. The approach unifies, generalizes and improves on
the existing results for both parametric and nonparametric change-point
estimation, applied to independent, short-range dependent and as well
long-range dependent sequences.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th