Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics for change-point models under varying degrees of
  mis-specification   Change-point models are widely used by statisticians to model drastic changes
in the pattern of observed data. Least squares/maximum likelihood based
estimation of change-points leads to curious asymptotic phenomena. When the
change-point model is correctly specified, such estimates generally converge at
a fast rate ($n$) and are asymptotically described by minimizers of jump
process. Under complete mis-specification by a smooth curve, i.e. when a
change-point model is fitted to data described by a smooth curve, the rate of
convergence slows down to $n^{1/3}$ and the limit distribution changes to that
of the minimizer of a continuous Gaussian process. In this paper we provide a
bridge between these two extreme scenarios by studying the limit behavior of
change-point estimates under varying degrees of model mis-specification by
smooth curves, which can be viewed as local alternatives. We find that the
limiting regime depends on how quickly the alternatives approach a change-point
model. We unravel a family of `intermediate' limits that can transition, at
least qualitatively, to the limits in the two extreme scenarios.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat