| 000 | 03898cam a2200301Ii 4500 | ||
|---|---|---|---|
| 001 | 9780429488436 | ||
| 008 | 180706s2018 flu ob 001 0 eng d | ||
| 020 |
_a9780429948893 (e-book: PDF) _q(e-book : PDF) |
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| 024 | 7 |
_a10.1201/9780429488436 _2doi |
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| 035 | _a(OCoLC)1034626003 | ||
| 040 |
_aFlBoTFG _cFlBoTFG _erda |
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| 050 | 4 |
_aQA196.5 _b.B67 2018 |
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| 082 | 0 | 4 |
_a512.9434 _bB743 |
| 100 | 1 |
_aBose, Arup, _eauthor. _912622 |
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| 245 | 1 | 0 |
_aPatterned Random Matrices / _cArup Bose (Indian Statistical Institute, Kolkata, West Bengal, India). |
| 250 | _aFirst edition. | ||
| 264 | 1 |
_aBoca Raton, FL : _bCRC Press, _c2018. |
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| 300 | _a1 online resource (xxi, 267 pages) | ||
| 336 |
_atext _2rdacontent |
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| 337 |
_acomputer _2rdamedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 505 | 0 | 0 |
_tchapter 1 A unified framework / _r Arup Bose -- _tchapter 2 Common symmetric patterned matrices / _r Arup Bose -- _tchapter 3 Patterned matrices / _r Arup Bose -- _tchapter 4 k-Circulant matrices / _r Arup Bose -- _tchapter 5 Wigner-type matrices / _r Arup Bose -- _tchapter 6 Balanced Toeplitz and Hankel matrices / _r Arup Bose -- _tchapter 7 Patterned band matrices / _r Arup Bose -- _tchapter 8 Triangular matrices / _r Arup Bose -- _tchapter 9 Joint convergence of i.i.d. patterned matrices / _r Arup Bose -- _tchapter 10 Joint convergence of independent patterned matrices / _r Arup Bose -- _tchapter 11 Autocovariance matrix / _r Arup Bose. |
| 520 | _a"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. | ||
| 650 | 0 |
_aRandom matrices. _912623 |
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| 776 | 0 | 8 |
_iPrint version: _z9781138591462 |
| 856 | 4 | 0 |
_uhttps://www.taylorfrancis.com/books/9780429948893 _zClick here to view. |
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_c70257 _d70257 |
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