Author | Andersen, H. H. author |
---|---|
Title | Linear and Graphical Models [electronic resource] : for the Multivariate Complex Normal Distribution / by H. H. Andersen, M. Hรธjbjerre, D. Sรธrensen, P. S. Eriksen |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4240-6 |
Descript | 183 p. online resource |
1 Prerequisites -- 1.1 Complex Matrix Algebra -- 1.2 A Vector Space Isomorphism -- 1.3 Complex Random Variables -- 1.4 Complex Random Vectors and Matrices -- 2 The Multivariate Complex Normal Distribution -- 2.1 The Univariate Complex Normal Distribution -- 2.2 The Multivariate Complex Normal Distribution -- 2.3 Independence, Marginal and Conditional Distributions -- 2.4 The Multivariate Complex Normal Distribution in Matrix Notation -- 3 The Complex Wishart Distribution and the Complex U-distribution -- 3.1 The Complex Wishart Distribution -- 3.2 The Complex U-distribution -- 4 Multivariate Linear Complex Normal Models -- 4.1 Complex MANOVA Models -- 4.2 Maximum Likelihood Estimation in Complex MANOVA Models -- 4.3 Hypothesis Testing in Complex MANOVA Models -- 5 Simple Undirected Graphs -- 6 Conditional Independence and Markov Properties -- 6.1 Conditional Independence -- 6.2 Markov Properties in Relation to Simple Undirected Graphs -- 7 Complex Normal Graphical Models -- 7.1 Notation -- 7.2 The Concentration Matrix -- 7.3 Complex Normal Graphical Models -- 7.4 Maximum Likelihood Estimation of the Concentration Matrix -- 7.5 Decomposition of the Estimation Problem -- 7.6 Hypothesis Testing in Complex Normal Graphical Models -- A Complex Matrices -- A.1 Complex Vector Space -- A.2 Basic Operations of Complex Matrices -- A.3 Inverse Matrix -- A.4 Determinant and Eigenvalues -- A.5 Trace and Rank -- A.6 Conjugate Transpose Matrix -- A.7 Hermitian Matrix -- A.8 Unitary Matrix -- A.9 Positive Semidefinite Complex Matrices -- A.10 Positive Definite Complex Matrices -- A.11 Direct Product -- A.12 Partitioned Complex Matrices -- B Orthogonal Projections -- Notation