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High-Dimensional Covariance Estimation

ISBN-10: 1118034295

ISBN-13: 9781118034293

Edition: 2013

Authors: Mohsen Pourahmadi

List price: $136.95
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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.
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Book details

List price: $136.95
Copyright year: 2013
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/21/2013
Binding: Hardcover
Pages: 208
Size: 6.25" wide x 9.75" long x 0.75" tall
Weight: 1.254
Language: English

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