
Contents
-
-
-
-
-
-
-
-
-
-
-
-
-
Abstract Abstract
-
28.1 Introduction 28.1 Introduction
-
28.1.1 Two spectral statistical techniques: PCA and CCA 28.1.1 Two spectral statistical techniques: PCA and CCA
-
28.1.2 Classical theory, modern questions 28.1.2 Classical theory, modern questions
-
-
28.2 Wishart distribution and normal theory 28.2 Wishart distribution and normal theory
-
28.2.1 Classical results, distribution of eigenvalues 28.2.1 Classical results, distribution of eigenvalues
-
28.2.2 Classical asymptotics: fixed p, large n 28.2.2 Classical asymptotics: fixed p, large n
-
28.2.3 An application in optimization and finance 28.2.3 An application in optimization and finance
-
-
28.3 Extreme eigenvalues, Tracy–Widom laws 28.3 Extreme eigenvalues, Tracy–Widom laws
-
28.3.1 Statistical motivation: largest root tests in PCA 28.3.1 Statistical motivation: largest root tests in PCA
-
28.3.2 Tracy–Widom convergence 28.3.2 Tracy–Widom convergence
-
28.3.3 Possible applications to model selection 28.3.3 Possible applications to model selection
-
-
28.4 Limiting spectral distribution results 28.4 Limiting spectral distribution results
-
28.4.1 Limiting spectra of sample covariance matrices 28.4.1 Limiting spectra of sample covariance matrices
-
28.4.2 Robustness questions 28.4.2 Robustness questions
-
-
28.5 Conclusion 28.5 Conclusion
-
Acknowledgements Acknowledgements
-
References References
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
28 Multivariate statistics
Get accessNoureddine El Karoui, University of California, Berkeley, Department of Statistics, 367 Evans Hall, Berkeley, CA 94720-3860, USA, nkaroui@ stat.berkeley.edu
-
Published:08 August 2018
Cite
Abstract
This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical techniques, principal components analysis (PCA) and canonical correlation analysis (CCA), before discussing the Wishart distribution and normal theory. It then describes extreme eigenvalues and Tracy–Widom laws, taking into account the results obtained in the asymptotic setting of ‘large p, large n’. It also analyses the results for the limiting spectra of sample covariance matrices..
Sign in
Personal account
- Sign in with email/username & password
- Get email alerts
- Save searches
- Purchase content
- Activate your purchase/trial code
- Add your ORCID iD
Purchase
Our books are available by subscription or purchase to libraries and institutions.
Purchasing informationMonth: | Total Views: |
---|---|
October 2022 | 1 |
December 2022 | 10 |
February 2023 | 3 |
March 2023 | 2 |
May 2023 | 3 |
June 2023 | 3 |
August 2023 | 2 |
September 2023 | 5 |
November 2023 | 3 |
December 2023 | 2 |
January 2024 | 3 |
February 2024 | 4 |
March 2024 | 7 |
April 2024 | 2 |
June 2024 | 2 |
July 2024 | 5 |
September 2024 | 4 |
December 2024 | 1 |
January 2025 | 2 |
February 2025 | 4 |
March 2025 | 5 |
April 2025 | 7 |
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.