Large Covariance and Autocovariance Matrices(Chapman & Hall/CRC Monographs on Statistics and Applied Probability) H 296 p. 18
Bose, Arup, Bhattacharjee, Monika 著
目次
LARGE COVARIANCE MATRIX I Consistency Covariance classes and regularization Covariance classes Covariance regularization Bandable Σp Parameter space Estimation in U Minimaxity Toeplitz Σp Parameter space Estimation in Gβ (M) or Fβ (M0, M) Minimaxity Sparse Σp Parameter space Estimation in Uτ (q, C0(p), M ) or Gq (Cn,p) Minimaxity LARGE COVARIANCE MATRIX II Bandable Σp Models and examples Weak dependence Estimation Sparse Σp LARGE AUTOCOVARIANCE MATRIX III Models and examples Estimation of Γ0,p Estimation of Γu,p Parameter spaces Estimation Estimation in MA(r) Estimation in IVAR(r) Gaussian assumption Simulations SPECTRAL DISTRIBUTION LSD Moment method Method of Stieltjes transform Wigner matrix: semi-circle law Independent matrix: Marčenko -Pastur law Results on Z: p/n → y > 0 Results on Z: p/n → 0 NON-COMMUTATIVE PROBABILITY NCP and its convergence Essentials of partition theory Möbius function Partition and non-crossing partition Kreweras complement Free cumulant; free independence Moments of free variables Joint convergence of random matrices Compound free Poisson GENERALIZED COVARIANCE MATRIX I Preliminaries Assumptions Embedding NCP convergence Main idea Main convergence LSD of symmetric polynomials Stieltjes transform Corollaries GENERALIZED COVARIANCE MATRIX II Preliminaries Assumptions Centering and Scaling Main idea NCP convergence LSD of symmetric polynomials Stieltjes transform Corollaries SPECTRA OF AUTOCOVARIANCE MATRIX I Assumptions LSD when p/n → y ∈ (0, ∞) MA(q), q < ∞ MA(∞) Application to specific cases LSD when p/n → 0 Application to specific cases Non-symmetric polynomials SPECTRA OF AUTOCOVARIANCE MATRIX II Assumptions LSD when p/n → y ∈ (0, ∞) MA(q), q < ∞ MA(∞) LSD when p/n → 0 MA(q), q < ∞ MA(∞) GRAPHICAL INFERENCE MA order determination AR order determination Graphical tests for parameter matrices TESTING WITH TRACE One sample trace Two sample trace Testing SUPPLEMENTARY PROOFS Proof of Lemma Proof of Theorem (a) Proof of Theorem Proof of Lemma Proof of Corollary (c) Proof of Corollary (c) Proof of Corollary (c) Proof of Lemma Proof of Lemma Lemmas for Theorem