4,074 research outputs found
FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control
Large-scale multiple testing with correlated and heavy-tailed data arises in
a wide range of research areas from genomics, medical imaging to finance.
Conventional methods for estimating the false discovery proportion (FDP) often
ignore the effect of heavy-tailedness and the dependence structure among test
statistics, and thus may lead to inefficient or even inconsistent estimation.
Also, the commonly imposed joint normality assumption is arguably too stringent
for many applications. To address these challenges, in this paper we propose a
Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for large-scale
simultaneous inference with control of the false discovery proportion. We
demonstrate that robust factor adjustments are extremely important in both
controlling the FDP and improving the power. We identify general conditions
under which the proposed method produces consistent estimate of the FDP. As a
byproduct that is of independent interest, we establish an exponential-type
deviation inequality for a robust -type covariance estimator under the
spectral norm. Extensive numerical experiments demonstrate the advantage of the
proposed method over several state-of-the-art methods especially when the data
are generated from heavy-tailed distributions. The proposed procedures are
implemented in the R-package FarmTest.Comment: 52 pages, 9 figure
Revisiting the distance, environment and supernova properties of SNR G57.2+0.8 that hosts SGR 1935+2154
We have performed a multi-wavelength study of supernova remnant (SNR)
G57.2+0.8 and its environment. The SNR hosts the magnetar SGR 1935+2154, which
emitted an extremely bright ms-duration radio burst on 2020 Apr 28 (The
Chime/Frb Collaboration et al. 2020; Bochenek et al. 2020). We used the 12CO
and 13CO J=1-0 data from the Milky Way Image Scroll Painting (MWISP) CO line
survey to search for molecular gas associated with G57.2+0.8, in order to
constrain the physical parameters (e.g., the distance) of the SNR and its
magnetar. We report that SNR G57.2+0.8 is likely impacting the molecular clouds
(MCs) at the local standard of rest (LSR) velocity V_{LSR} ~ 30 km/s and
excites a weak 1720 MHz OH maser with a peak flux density of 47 mJy/beam. The
chance coincidence of a random OH spot falling in the SNR is <12%, and the
OH-CO correspondence chance is 7% at the maser spot. This combines to give < 1%
false probability of the OH maser, suggesting a real maser detection. The LSR
velocity of the MCs places the SNR and magnetar at a kinematic distance of
d=6.6 +/- 0.7 kpc. The nondetection of thermal X-ray emission from the SNR and
the relatively dense environment suggests G57.2+0.8 be an evolved SNR with an
age (d/6.6 kpc) yr. The explosion energy of G57.2+0.8 is
lower than erg,
which is not very energetic even assuming a high ambient density = 10
cm. This reinforces the opinion that magnetars do not necessarily result
from very energetic supernova explosions.Comment: 9 pages, 5 figures, accepted for publication in the Astrophysical
Journa
User-Friendly Covariance Estimation for Heavy-Tailed Distributions
We offer a survey of recent results on covariance estimation for heavy-tailed
distributions. By unifying ideas scattered in the literature, we propose
user-friendly methods that facilitate practical implementation. Specifically,
we introduce element-wise and spectrum-wise truncation operators, as well as
their -estimator counterparts, to robustify the sample covariance matrix.
Different from the classical notion of robustness that is characterized by the
breakdown property, we focus on the tail robustness which is evidenced by the
connection between nonasymptotic deviation and confidence level. The key
observation is that the estimators needs to adapt to the sample size,
dimensionality of the data and the noise level to achieve optimal tradeoff
between bias and robustness. Furthermore, to facilitate their practical use, we
propose data-driven procedures that automatically calibrate the tuning
parameters. We demonstrate their applications to a series of structured models
in high dimensions, including the bandable and low-rank covariance matrices and
sparse precision matrices. Numerical studies lend strong support to the
proposed methods.Comment: 56 pages, 2 figure
From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration
In this paper, we propose a novel approach to the rank minimization problem,
termed rank residual constraint (RRC) model. Different from existing low-rank
based approaches, such as the well-known nuclear norm minimization (NNM) and
the weighted nuclear norm minimization (WNNM), which estimate the underlying
low-rank matrix directly from the corrupted observations, we progressively
approximate the underlying low-rank matrix via minimizing the rank residual.
Through integrating the image nonlocal self-similarity (NSS) prior with the
proposed RRC model, we apply it to image restoration tasks, including image
denoising and image compression artifacts reduction. Towards this end, we first
obtain a good reference of the original image groups by using the image NSS
prior, and then the rank residual of the image groups between this reference
and the degraded image is minimized to achieve a better estimate to the desired
image. In this manner, both the reference and the estimated image are updated
gradually and jointly in each iteration. Based on the group-based sparse
representation model, we further provide a theoretical analysis on the
feasibility of the proposed RRC model. Experimental results demonstrate that
the proposed RRC model outperforms many state-of-the-art schemes in both the
objective and perceptual quality
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