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El. knyga: Spectral Theory of Large Dimensional Random Matrices and its Applications to Wireless Communications and Finance: Random Matrix Theory and its Applications [World Scientific e-book]

(Univ Of Sci & Tech Of China, China), (Northeast Normal Univ, China & Nus, S'pore), (Inst For Infocomm Research, S'pore)
  • Formatas: 232 pages
  • Išleidimo metai: 27-Mar-2014
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814579063
Kitos knygos pagal šią temą:
  • World Scientific e-book
  • Kaina: 114,58 €*
  • * this price gives unlimited concurrent access for unlimited time
Spectral Theory of Large Dimensional Random Matrices and its Applications to Wireless Communications and Finance: Random Matrix Theory and its ApplicationsDidesnis paveikslėlis
  • Formatas: 232 pages
  • Išleidimo metai: 27-Mar-2014
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814579063
Kitos knygos pagal šią temą:
World Scientific e-booksMore info about World Scientific e-books
Partnerių interneto svetainė: http://www.worldscientific.com/worldscibooks/10.1142/9049#t=toc
The spectral analysis of large dimensional random matrices--random matrix theory (RMT)--is currently the only systematic theory that can be applied to some problems of large dimensional data analysis, say Bai, Fang, and Liang. They introduce the basic concepts and results of the theory and some applications in wireless communications and financial statistics. The material would be accessible to graduate students and beginning researchers interested in applying RMT to their own research areas. Only outlines of proofs are provided for the theorems, with reference to where detailed proofs can be found. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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 distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.
1 Introduction
1(10)
1.1 History of RMT and Current Development
1(5)
1.1.1 A brief review of RMT
2(1)
1.1.2 Spectral Analysis of Large Dimensional Random Matrices
3(1)
1.1.3 Limits of Extreme Eigenvalues
4(1)
1.1.4 Convergence Rate of ESD
4(1)
1.1.5 Circular Law
5(1)
1.1.6 CLT of Linear Spectral Statistics
5(1)
1.1.7 Limiting Distributions of Extreme Eigenvalues and Spacings
6(1)
1.2 Applications to Wireless Communications
6(1)
1.3 Applications to Finance Statistics
7(4)
2 Limiting Spectral Distributions
11(50)
2.1 Semicircular Law
11(11)
2.1.1 The iid Case
12(6)
2.1.2 Independent but not Identically Distributed
18(4)
2.2 Marcenko-Pastur Law
22(5)
2.2.1 MP Law for iid Case
22(3)
2.2.2 Generalization to the Non-iid Case
25(1)
2.2.3 Proof of Theorem 2.11 by Stieltjes Transform
26(1)
2.3 LSD of Products
27(16)
2.3.1 Existence of the ESD of Sn Tn
28(1)
2.3.2 Truncation of the ESD of Tn
29(1)
2.3.3 Truncation, Centralization and Rescaling of the X-variables
30(1)
2.3.4 Sketch of the Proof of Theorem 2.12
31(1)
2.3.5 LSD of F Matrix
32(4)
2.3.6 Sketch of the Proof of Theorem 2.14
36(6)
2.3.7 When T is a Wigner Matrix
42(1)
2.4 Hadamard Product
43(9)
2.4.1 Truncation and Centralization
48(2)
2.4.2 Outlines of Proof of the theorem
50(2)
2.5 Circular Law
52(9)
2.5.1 Failure of Techniques Dealing with Hermitian Matrices
53(2)
2.5.2 Revisit of Stieltjes Transformation
55(2)
2.5.3 A Partial Answer to the Circular Law
57(1)
2.5.4 Comments and Extensions of Theorem 2.33
58(3)
3 Extreme Eigenvalues
61(16)
3.1 Wigner Matrix
62(2)
3.2 Sample Covariance Matrix
64(2)
3.2.1 Spectral Radius
66(1)
3.3 Spectrum Separation
66(7)
3.4 Tracy-Widom Law
73(4)
3.4.1 TW Law for Wigner Matrix
73(1)
3.4.2 TW Law for Sample Covariance Matrix
74(3)
4 Central Limit Theorems of Linear Spectral Statistics
77(32)
4.1 Motivation and Strategy
77(2)
4.2 CLT of LSS for Wigner Matrix
79(11)
4.2.1 Outlines of the Proof
81(9)
4.3 CLT of LSS for Sample Covariance Matrices
90(8)
4.4 F Matrix
98(11)
4.4.1 Decomposition of Xnf
100(1)
4.4.2 Limiting Distribution of X†nf
101(2)
4.4.3 The Limiting Distribution of Xnf
103(6)
5 Limiting Behavior of Eigenmatrix of Sample Covariance Matrix
109(24)
5.1 Earlier Work by Silverstein
110(2)
5.2 Further extension of Silverstein's Work
112(5)
5.3 Projecting the Eigenmatrix to a d-dimensional Space
117(16)
5.3.1 Main Results
119(4)
5.3.2 Sketch of Proof of Theorem 5.19
123(9)
5.3.3 Proof of Corollary 5.23
132(1)
6 Wireless Communications
133(22)
6.1 Introduction
133(2)
6.2 Channel Models
135(8)
6.2.1 Basics of Wireless Communication Systems
135(1)
6.2.2 Matrix Channel Models
136(1)
6.2.3 Random Matrix Channels
137(2)
6.2.4 Linearly Precoded Systems
139(4)
6.3 Channel Capacity for MIMO Antenna Systems
143(8)
6.3.1 Single-Input Single-Output Channels
143(2)
6.3.2 MIMO Fading Channels
145(6)
6.4 Limiting Capacity of Random MIMO Channels
151(3)
6.4.1 CSI-Unknown Case
152(1)
6.4.2 CSI-Known Case
153(1)
6.5 Concluding Remarks
154(1)
7 Limiting Performances of Linear and Iterative Receivers
155(22)
7.1 Introduction
155(1)
7.2 Linear Equalizers
156(2)
7.2.1 ZF Equalizer
157(1)
7.2.2 Matched Filter (MF) Equalizer
157(1)
7.2.3 MMSE Equalizer
157(1)
7.2.4 Suboptimal MMSE Equalizer
158(1)
7.3 Limiting SINR Analysis for Linear Receivers
158(7)
7.3.1 Random Matrix Channels
158(3)
7.3.2 Linearly Precoded Systems
161(2)
7.3.3 Asymptotic SINR Distribution
163(2)
7.4 Iterative Receivers
165(4)
7.4.1 MMSE-SIC
165(3)
7.4.2 BI-GDFE
168(1)
7.5 Limiting Performance of Iterative Receivers
169(4)
7.5.1 MMSE-SIC Receiver
170(1)
7.5.2 BI-GDFE Receiver
171(2)
7.6 Numerical Results
173(2)
7.7 Concluding Remarks
175(2)
8 Application to Finance
177(24)
8.1 Portfolio and Risk Management
177(6)
8.1.1 Markowitz's Portfolio Selection
177(2)
8.1.2 Financial Correlations and Information Extracting
179(4)
8.2 Factor Models
183(11)
8.2.1 From PCA to Generalized Dynamic Factor Models
184(3)
8.2.2 CAPM and APT
187(1)
8.2.3 Determine the Number of Factors
188(6)
8.3 Some Application in Finance of Factor Model
194(7)
8.3.1 Inflation Forecasting
194(2)
8.3.2 Leading and Coincident Index
196(2)
8.3.3 Financial Crises Warning
198(3)
References 201(16)
Index 217
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