Random matrix theory in statistics: A review

By Debashis Paul, Alexander Aue. 2014

205 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d70c576a8e06c55c7d5db619d68326f826c2794

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Clifford Lam
2. Qiwei Yao
3. Zeng Li
4. Jianfeng Yao
5. Haoyang Liu
6. Xiucai Ding
7. Fan Yang
8. Debashis Paul

In Mathematical Physics

1. Xiucai Ding
2. Fan Yang
3. Zeng Li
4. Clifford Lam
5. Haoyang Liu
6. Debashis Paul
7. Alexander Aue
8. Jianfeng Yao

In Statistics and Probability

1. Xiucai Ding
2. Zeng Li
3. Alexander Aue
4. Jianfeng Yao
5. Clifford Lam
6. Debashis Paul
7. Fan Yang
8. Michael W. Mahoney

Citations in the corpus

• Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, background): “7 Several overviews of RMT are available [143, 41, 71, 142, 22, 42, 110, 24].”
• A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices (2016, background): “For a detailed review, one can refer to [18, 28, 39].”
• Alternative asymptotics for cointegration tests in large VARs (2016, background): “where ∆1 and ∆2 are as defined in (31) and (32).”
• Cleaning large correlation matrices: tools from random matrix theory (2016, background): “Whereas the Wigner Ensemble has been the subject of a large amount of studies in physics [50], results on the Wishart Ensemble mostly come from mathematics & statistics [18,56,93,94], telecommunication [57] or the financial/econophysics literature [24,29,67], although some work in the physics litera”
• Spiked separable covariance matrices and principal components (2019, background): “Later on the convergence result of the ESD is extended to various settings with general positive definite covariance matrices r A; we refer the readers to the monograph [3] and the review paper [46].”
• On the Marčenko-Pastur law for linear time series (2013, methodology): “The proof techniques for establishing large-sample results about F̂τ are based on exploiting convergence properties of Stieltjes transforms, which continue to play an important role in verifying theoretical results in RMT; see, for example, Paul and Aue [30] for a recent summary.”
• On testing for high-dimensional white noise (2018, methodology): “For a review on such progress, we refer to [21], [30] and monograph [40].”