Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frequency Detection and Change Point Estimation for Time Series of
  Complex Oscillation   We consider detecting the evolutionary oscillatory pattern of a signal when
it is contaminated by non-stationary noises with complexly time-varying data
generating mechanism. A high-dimensional dense progressive periodogram test is
proposed to accurately detect all oscillatory frequencies. A further
phase-adjusted local change point detection algorithm is applied in the
frequency domain to detect the locations at which the oscillatory pattern
changes. Our method is shown to be able to detect all oscillatory frequencies
and the corresponding change points within an accurate range with a prescribed
probability asymptotically. This study is motivated by oscillatory frequency
estimation and change point detection problems encountered in physiological
time series analysis. An application to spindle detection and estimation in
sleep EEG data is used to illustrate the usefulness of the proposed
methodology. A Gaussian approximation scheme and an overlapping-block
multiplier bootstrap methodology for sums of complex-valued high dimensional
non-stationary time series without variance lower bounds are established, which
could be of independent interest.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat