Patterned Random Matrices - Tapa blanda

Bose, Arup

 
9780367734466: Patterned Random Matrices
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ISBN 10: 036773446X ISBN 13: 9780367734466
Editorial: Chapman and Hall/CRC, 2020

Sinopsis

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 Marchenko-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.

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Acerca del autor

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.

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Editorial
Chapman and Hall/CRC
Año de publicación
2020
Idioma
Inglés
ISBN 10 
036773446X
ISBN 13 
9780367734466
Encuadernación
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Número de edición
1
Número de páginas
292
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9781138591462: Patterned Random Matrices

Edición Destacada

ISBN 10:  1138591467 ISBN 13:  9781138591462
Editorial: Chapman and Hall/CRC, 2018
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