Patterned Random Matrices / (Record no. 70257)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 03898cam a2200301Ii 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780429488436 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 180706s2018 flu ob 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429948893 (e-book: PDF) |
| -- | (e-book : PDF) |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 512.9434 |
| -- | B743 |
| 100 1# - AUTHOR NAME | |
| Author | Bose, Arup, |
| 245 10 - TITLE STATEMENT | |
| Title | Patterned Random Matrices / |
| 250 ## - EDITION STATEMENT | |
| Edition statement | First edition. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (xxi, 267 pages) |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | "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 Sankyh 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."--Provided by publisher. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.taylorfrancis.com/books/9780429948893 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Boca Raton, FL : |
| -- | CRC Press, |
| -- | 2018. |
| 336 ## - | |
| -- | text |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | rdacarrier |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Random matrices. |
No items available.