31,543 research outputs found
Challenges of Big Data Analysis
Big Data bring new opportunities to modern society and challenges to data
scientists. On one hand, Big Data hold great promises for discovering subtle
population patterns and heterogeneities that are not possible with small-scale
data. On the other hand, the massive sample size and high dimensionality of Big
Data introduce unique computational and statistical challenges, including
scalability and storage bottleneck, noise accumulation, spurious correlation,
incidental endogeneity, and measurement errors. These challenges are
distinguished and require new computational and statistical paradigm. This
article give overviews on the salient features of Big Data and how these
features impact on paradigm change on statistical and computational methods as
well as computing architectures. We also provide various new perspectives on
the Big Data analysis and computation. In particular, we emphasis on the
viability of the sparsest solution in high-confidence set and point out that
exogeneous assumptions in most statistical methods for Big Data can not be
validated due to incidental endogeneity. They can lead to wrong statistical
inferences and consequently wrong scientific conclusions
Generic continuous spectrum for multi-dimensional quasi periodic Schr\"odinger operators with rough potentials
We study the multi-dimensional operator , where is the shift of the torus
\T^d. When , we show the spectrum of is almost surely purely
continuous for a.e. and generic continuous potentials. When ,
the same result holds for frequencies under an explicit arithmetic criterion.
We also show that general multi-dimensional operators with measurable
potentials do not have eigenvalue for generic
Robust Inference of Risks of Large Portfolios
We propose a bootstrap-based robust high-confidence level upper bound (Robust
H-CLUB) for assessing the risks of large portfolios. The proposed approach
exploits rank-based and quantile-based estimators, and can be viewed as a
robust extension of the H-CLUB method (Fan et al., 2015). Such an extension
allows us to handle possibly misspecified models and heavy-tailed data. Under
mixing conditions, we analyze the proposed approach and demonstrate its
advantage over the H-CLUB. We further provide thorough numerical results to
back up the developed theory. We also apply the proposed method to analyze a
stock market dataset.Comment: 45 pages, 2 figure
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