Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cleaning large correlation matrices: tools from random matrix theory   This review covers recent results concerning the estimation of large
covariance matrices using tools from Random Matrix Theory (RMT). We introduce
several RMT methods and analytical techniques, such as the Replica formalism
and Free Probability, with an emphasis on the Marchenko-Pastur equation that
provides information on the resolvent of multiplicatively corrupted noisy
matrices. Special care is devoted to the statistics of the eigenvectors of the
empirical correlation matrix, which turn out to be crucial for many
applications. We show in particular how these results can be used to build
consistent "Rotationally Invariant" estimators (RIE) for large correlation
matrices when there is no prior on the structure of the underlying process. The
last part of this review is dedicated to some real-world applications within
financial markets as a case in point. We establish empirically the efficacy of
the RIE framework, which is found to be superior in this case to all previously
proposed methods. The case of additively (rather than multiplicatively)
corrupted noisy matrices is also dealt with in a special Appendix. Several open
problems and interesting technical developments are discussed throughout the
paper.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph