High-Dimensional Covariance Estimation - Wiley Probability and Statistics by Mohsen Pourahmadi Hardcover

About the Book

"Focusing on methodology and computation more than on theorems and proofs, this book provides computationally feasible and statistically efficient methods for estimating sparse and large covariance matrices of high-dimensional data. Extensive in breadth and scope, it features ample applications to a number of applied areas, including business and economics, computer science, engineering, and financial mathematics; recognizes the important and significant contributions of longitudinal and spatial data; and includes various computer codes in R throughout the text and on an author-maintained web site"--

Book Synopsis

Methods for estimating sparse and large covariance matrices

Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning.

Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task.

High-Dimensional Covariance Estimation features chapters on:

• Data, Sparsity, and Regularization
• Regularizing the Eigenstructure
• Banding, Tapering, and Thresholding
• Covariance Matrices
• Sparse Gaussian Graphical Models
• Multivariate Regression

The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

From the Back Cover

Methods for estimating sparse and large covariance matrices

Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning.

Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task.

High-Dimensional Covariance Estimation features chapters on:

• Data, Sparsity, and Regularization
• Regularizing the Eigenstructure
• Banding, Tapering, and Thresholding
• Covariance Matrices
• Sparse Gaussian Graphical Models
• Multivariate Regression

The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

About the Author

MOHSEN POURAHMADI, PhD, is Professor of Statistics at Texas A&M University. He is an elected member of the International Statistical Institute, a Fellow of the American Statistical Association, and a member of the American Mathematical Society. Dr. Pourahmadi is the author of Foundations of Time Series Analysis and Prediction Theory, also published by Wiley.