Last edited by Meztiran
Wednesday, July 8, 2020 | History

6 edition of Spectral analysis of large dimensional random matrices found in the catalog.

Spectral analysis of large dimensional random matrices

by Zhidong Bai

  • 37 Want to read
  • 37 Currently reading

Published by Springer in New York, London .
Written in English

    Subjects:
  • Random matrices,
  • Spectrum analysis

  • Edition Notes

    Includes bibliographical references (p. 533-546) and index.

    StatementZhidong Bai, Jack W. Silverstein.
    SeriesSpringer series in statistics, Springer series in statistics
    ContributionsSilverstein, Jack W.
    Classifications
    LC ClassificationsQA188 .B33 2010
    The Physical Object
    Paginationxvi, 551 p. :
    Number of Pages551
    ID Numbers
    Open LibraryOL24098701M
    ISBN 101441906606
    ISBN 109781441906601
    LC Control Number2009942423

    () Signal detection via spectral theory of large dimensional random matrices. IEEE Transactions on Signal Processing , () Addition of freely independent random by: Some special methodologies are developed for spectral analysis of large dimensional quaternion self-dual matrices. Abstract Since E.P. Wigner () established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random by:

    Spectral analysis of large random matrices plays an important role in multivariate sta-tistical estimation and testing problems. For example, variances of the principal compo-nents are functions of covariance eigenvalues (Muirhead,), and Roy’s largest root test statistic is the spectral distance between the sample covariance and its.   Spectral properties of large dimensional random matrices I'll try to explain what the above graphs represent. The histogram in the first one is that of the eigenvalues of a sample covariance matrix (s.c.m.) formed from samples of a dimensional random vector whose population covariance matrix has 3 distinct eigenvalues: 1, 3, and

    R. Brent Dozier, Jack W. Silverstein, Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices, Journal of Multivariate Analysis, v n.6, p, July, Cited by: Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the multiplicity of the smallest eigenvalue of the spatial covariance matrix R of the sensed data.


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Spectral analysis of large dimensional random matrices by Zhidong Bai Download PDF EPUB FB2

The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of by: The aim of the book is to introduce basic concepts, main results, Spectral analysis of large dimensional random matrices book widely applied mathematical tools in the spectral analysis of large dimensional random matrices.

The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices.

The core of the book focuses. Journal of the Royal Statistical Society: Series A (Statistics in Society) Journal of the Royal Statistical Society: Series B (Statistical Methodology) Book reviews. Spectral Analysis of Large Dimensional Random Matrices, 2nd edn.

Cedric E. by:   The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance.

In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral. The moment approach to establishing limiting theorems for spectral analysis of large dimensional random matrices is to show that each moment of the ESD tends to a nonrandom limit.

This proves the existence of the LSD by applying the Carleman criterion. This method successfully established the existence of the LSD. One pioneering work is Wigner’s semicircular law for a Gaussian (or Wigner) matrix (Wigner (, )).

He proved that the expected ESD of a large dimensional Wigner matrix tends to the so-called semicircular law. This work was generalized by Arnold (, ) and Grenander () in various aspects. Definition 2 Let {An}∞ n=1 be a sequence of square matrices with the corresponding ESD {Pn}∞ n=1.

The Limiting Spectral Distribution (or measure) (LSD) of the se- quence is defined as the weak limit of the sequence {Pn}, if it exists.

Abstract: In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering.

In this paper, we study the spectral properties of the large block random matrices when the blocks are general rectangular matrices. Under some moment assumptions of the underlying distributions, we prove the existence of the limiting spectral distribution (LSD) of the block random matrices.

Further, we determine the Stieltjes transform of the LSD under Cited by: 7. China Scientific Books Spectral Analysis of Large Dimensional Random Matrices - Mathematics Monograph Series 15 - Author: Zhidong Bai, Jack steinLanguage: EnglishISBN/ISSN: Published on: HardcoverThe aim of the book is to introduce basic concepts,main results,and widely applied mathematical tools in the spectral analysis of large dimensional ran dom matrices.

Spectral Analysis of Large Dimensional Random Matrices: : Bai, Zhidong, Silverstein, Jack W.: Libri in altre lingueAuthor: Zhidong Bai. This text introduces basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices.

It focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science.

In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices. Abstract. In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices.

Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering. Spectral Analysis of Large Dimensional Random Matrices - p This book introduces basic concepts main results and widely-applied mathematical tools in the spectral analysis o (EAN) bei The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the Spectral analysis of large dimensional random matrices.

The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. 'This book deals with the analysis of covariance matrices under two different assumptions: large-sample theory and high-dimensional-data theory.

While the former approach is the classical framework to derive asymptotics, nevertheless the latter has received increasing attention due to its applications in the emerging field of by: eigenvalues of a random matrix, noncentral Hermitian matrix, spectral analysis of large dimensional random matrices, spectral radius.

Introduction The necessity of studying the spectra of LDRM (Large Dimensional Ran dom Matrices), especially the Wigner matrices, arose in nuclear physics during the 's. Jack W.

Silverstein is the author of Spectral Analysis of Large Dimensional Random Matrices ( avg rating, 0 ratings, 0 reviews, published ). Eigenvalue distribution of large random matrices / Leonid Pastur, Mariya Shcherbina. p. cm. — (Mathematical surveys and monographs ; v.

) Includes bibliographical references and index. ISBN (alk. paper) 1. Distribution (Probability theory) 2. Random matrices. I. Shcherbina, Mariya, – II. Title. QAP File Size: KB.For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix Σ n let S ̃ n denote the usual sample covariance (centered by the mean) and S n the non-centered sample covariance matrix (i.e.

the matrix of second moment estimates), where p > this paper, we provide the limiting spectral distribution and central Cited by: 7.Spectral Analysis of Large Dimensional Random Matrices - The aim of the book is to introduce basic concepts main results and widely applied mathematical tools in the spectr (EAN) bei