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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:
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.
PART I MOTIVATION AND THE BASICS
1 Introduction 3
1.1 Least-Squares and Regularized Regression 4
1.2 Lasso: Survival of the Bigger 6
1.3 Thresholding the Sample Covariance Matrix 9
1.4 Sparse PCA and Regression 10
1.5 Graphical Models: Nodewise Regression 12
1.6 Cholesky Decomposition and Regression 13
1.7 The Bigger Picture: Latent Factor Models 14
1.8 Further Reading 16
2 Data, Sparsity and Regularization 21
2.1 Data Matrix: Examples 22... MORE
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.