2,206 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
On Studies of the Representation of Islam and the Muslims in West Media and Factors behind Misrepresentation
The subject of Islam and the Muslim is an important agenda under the volatile international situation, which drawing increasing attention worldwide with the impact of media report. Moreover, in-depth studies of Islam and the Muslim are blossoming to critically unravel the way Islam and the Muslim is represented in western discourse. This article presents a literature review of those studies of Islam and the Muslim, aiming to conclude respectively previous studies of representations of Islam and the Muslims and then to clarify the factors behind the misrepresentation, including historical factors, cultural factors, political factors and religious factors
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
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