دانلود کتاب Large Covariance and Autocovariance Matrices

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Content: Cover
Half title
Editors
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
Introduction
Part I
Chapter 1 LARGE COVARIANCE MATRIX I
1.1 Consistency
1.2 Covariance classes and regularization
1.2.1 Covariance classes
1.2.2 Covariance regularization
1.3 Bandable p
1.3.1 Parameter space
1.3.2 Estimation in U
1.3.3 Minimaxity
1.4 Toeplitz p
1.4.1 Parameter space
1.4.2 Estimation in G (M) or F (M0
M)
1.4.3 Minimaxity
1.5 Sparse p
1.5.1 Parameter space
1.5.2 Estimation in U˝ (q
C0(p)
M) or Gq(Cn
p)
1.5.3 Minimaxity
Chapter 2 LARGE COVARIANCE MATRIX II 2.1 Bandable p2.1.1 Models and examples
2.1.2 Weak dependence
2.1.3 Estimation
2.2 Sparse p
Chapter 3 LARGE AUTOCOVARIANCE MATRIX
3.1 Models and examples
3.2 Estimation of 0
p
3.3 Estimation of u
p
3.3.1 Parameter spaces
3.3.2 Estimation
3.4 Estimation in MA(r)
3.5 Estimation in IVAR(r)
3.6 Gaussian assumption
3.7 Simulations
Part II
Chapter 4 SPECTRAL DISTRIBUTION
4.1 LSD
4.1.1 Moment method
4.1.2 Method of Stieltjes transform
4.2 Wigner matrix: Semi-circle law
4.3 Independent matrix: Mar cenko{Pastur law
4.3.1 Results on Z: p=n ! y >
0 4.3.2 Results on Z: p=n ! 0Chapter 5 NON-COMMUTATIVE PROBABILITY
5.1 NCP and its convergence
5.2 Essentials of partition theory
5.2.1 MŁobius function
5.2.2 Partition and non-crossing partition
5.2.3 Kreweras complement
5.3 Free cumulant
free independence
5.4 Moments of free variables
5.5 Joint convergence of random matrices
5.5.1 Compound free Poisson
Chapter 6 GENERALIZED COVARIANCE MATRIX I
6.1 Preliminaries
6.1.1 Assumptions
6.1.2 Embedding
6.2 NCP convergence
6.2.1 Main idea
6.2.2 Main convergence
6.3 LSD of symmetric polynomials
6.4 Stieltjes transform 6.5 CorollariesChapter 7 GENERALIZED COVARIANCE MATRIX II
7.1 Preliminaries
7.1.1 Assumptions
7.1.2 Centering and Scaling
7.1.3 Main idea
7.2 NCP convergence
7.3 LSD of symmetric polynomials
7.4 Stieltjes transform
7.5 Corollaries
Part III
Chapter 8 SPECTRA OF AUTOCOVARIANCE MATRIX I
8.1 Assumptions
8.2 LSD when p=n ! y 2 (0
1)
8.2.1 MA(q), q <
1
8.2.2 MA(1)
8.2.3 Application to speci c cases
8.3 LSD when p=n ! 0
8.3.1 Application to speci c cases
8.4 Non-symmetric polynomials
Chapter 9 SPECTRA OF AUTOCOVARIANCE MATRIX II
9.1 Assumptions
9.2 LSD when p=n ! y 2 (0
1) 9.2.1 MA(q), q <
19.2.2 MA(1)
9.3 LSD when p=n ! 0
9.3.1 MA(q)
q <
1
9.3.2 MA(1)
Chapter 10 GRAPHICAL INFERENCE
10.1 MA order determination
10.2 AR order determination
10.3 Graphical tests for parameter matrices
Chapter 11 TESTING WITH TRACE
11.1 One sample trace
11.2 Two sample trace
11.3 Testing
Appendix: SUPPLEMENTARY PROOFS
A.1 Proof of Lemma 6.3.1
A.2 Proof of Theorem 6.4.1(a)
A.3 Proof of Theorem 7.2
A.4 Proof of Lemma 8.2.1
A.5 Proof of Corollary 8.2.1(c)
A.6 Proof of Corollary 8.2.4(c)
A.7 Proof of Corollary 8.3.1(c)
A.8 Proof of Lemma 8.2.2