Patterned Random Matrices

Nonfiction, Science & Nature, Mathematics, Probability, Algebra, Statistics
Cover of the book Patterned Random Matrices by Arup Bose, CRC Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Arup Bose ISBN: 9780429948886
Publisher: CRC Press Publication: May 23, 2018
Imprint: Chapman and Hall/CRC Language: English
Author: Arup Bose
ISBN: 9780429948886
Publisher: CRC Press
Publication: May 23, 2018
Imprint: Chapman and Hall/CRC
Language: English

Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications.

This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the Marchenko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices.

Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

 

 

 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications.

This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the Marchenko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices.

Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

 

 

 

More books from CRC Press

Cover of the book Mobile Cloud Computing by Arup Bose
Cover of the book Progress in Maritime Technology and Engineering by Arup Bose
Cover of the book A Concise Introduction to Hypercomplex Fractals by Arup Bose
Cover of the book Surgical SBAs for Finals with Explanatory Answers by Arup Bose
Cover of the book Polarized Light and the Mueller Matrix Approach by Arup Bose
Cover of the book Unity 4 Fundamentals by Arup Bose
Cover of the book Small Animal Dental, Oral and Maxillofacial Disease by Arup Bose
Cover of the book CRC Standard Curves and Surfaces with Mathematica by Arup Bose
Cover of the book An Introduction to Computational Risk Management of Equity-Linked Insurance by Arup Bose
Cover of the book Advances in SAR Remote Sensing of Oceans by Arup Bose
Cover of the book Parvoviruses and Human Disease by Arup Bose
Cover of the book Laboratory Techniques in Plant Bacteriology by Arup Bose
Cover of the book Digital Design in Action by Arup Bose
Cover of the book Handbook of Quantile Regression by Arup Bose
Cover of the book Turbomachinery Fluid Dynamics and Heat Transfer by Arup Bose
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy