Ebook: Linear and Graphical Models: for the Multivariate Complex Normal Distribution

In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.

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In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.

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In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.
Content:
Front Matter....Pages i-x
Prerequisites....Pages 1-13
The Multivariate Complex Normal Distribution....Pages 15-37
The Complex Wishart Distribution and the Complex U-distribution....Pages 39-66
Multivariate Linear Complex Normal Models....Pages 67-84
Simple Undirected Graphs....Pages 85-98
Conditional Independence and Markov Properties....Pages 99-113
Complex Normal Graphical Models....Pages 115-161
Back Matter....Pages 163-185

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In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.
Content:
Front Matter....Pages i-x
Prerequisites....Pages 1-13
The Multivariate Complex Normal Distribution....Pages 15-37
The Complex Wishart Distribution and the Complex U-distribution....Pages 39-66
Multivariate Linear Complex Normal Models....Pages 67-84
Simple Undirected Graphs....Pages 85-98
Conditional Independence and Markov Properties....Pages 99-113
Complex Normal Graphical Models....Pages 115-161
Back Matter....Pages 163-185
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