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| Preface | |
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| Motivation and the Basics | |
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| Introduction | |
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| Least Squares and Regularized Regression | |
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| Lasso: Survival of the Bigger | |
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| Thresholding the Sample Covariance Matrix | |
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| Sparse PCA and Regression | |
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| Graphical Models: Nodewise Regression | |
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| Cholesky Decomposition and Regression | |
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| The Bigger Picture: Latent Factor Models | |
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| Further Reading | |
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| Data, Sparsity, and Regularization | |
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| Data Matrix: Examples | |
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| Shrinking the Sample Covariance Matrix | |
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| Distribution of the Sample Eigenvalues | |
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| Regularizing Covariances Like a Mean | |
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| The Lasso Regression | |
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| Lasso: Variable Selection and Prediction | |
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| Lasso: Degrees of Freedom and BIC | |
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| Some Alternatives to the Lasso Penalty | |
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| Covariance Matrices | |
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| Definition and Basic Properties | |
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| The Spectral Decomposition | |
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| Structured Covariance Matrices | |
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| Functions of a Covariance Matrix | |
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| PCA: The Maximum Variance Property | |
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| Modified Cholesky Decomposition | |
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| Latent Factor Models | |
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| GLM for Covariance Matrices | |
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| GLM via the Cholesky Decomposition | |
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| GLM for Incomplete Longitudinal Data | |
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| The Incoherency Problem in Incomplete Longitudinal Data | |
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| The Incomplete Data and The EM Algorithm | |
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| A Data Example: Fruit Fly Mortality Rate | |
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| Simulating Random Correlation Matrices | |
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| Bayesian Analysis of Covariance Matrices | |
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| Covariance Estimation: Regularization | |
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| Regularizing the Eigenstructure | |
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| Shrinking the Eigenvalues | |
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| Regularizing The Eigenvectors | |
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| A Duality between PCA and SVD | |
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| Implementing Sparse PCA: A Data Example | |
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| Sparse Singular Value Decomposition (SSVD) | |
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| Consistency of PCA | |
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| Principal Subspace Estimation | |
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| Further Reading | |
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| Sparse Gaussian Graphical Models | |
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| Covariance Selection Models: Two Examples | |
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| Regression Interpretation of Entries of ∑<sup>-1</sup> | |
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| Penalized Likelihood and Graphical Lasso | |
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| Penalized Quasi-Likelihood Formulation | |
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| Penalizing the Cholesky Factor | |
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| Consistency and Sparsistency | |
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| Joint Graphical Models | |
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| Further Reading | |
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| Banding, Tapering, and Thresholding | |
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| Banding the Sample Covariance Matrix | |
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| Tapering the Sample Covariance Matrix | |
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| Thresholding the Sample Covariance Matrix | |
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| Low-Rank Plus Sparse Covariance Matrices | |
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| Further Reading | |
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| Multivariate Regression: Accounting for Correlation | |
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| Multivariate Regression and LS Estimators | |
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| Reduced Rank Regressions (RRR) | |
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| Regularized Estimation of B | |
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| Joint Regularization of (B, �) | |
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| Implementing MRCE: Data Examples | |
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| Intraday Electricity Prices | |
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| Predicting Asset Returns | |
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| Further Reading | |
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| Bibliography | |
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| Index | |