{"product_id":"highdimensional-covariance-estimation-9781118034293","title":"HighDimensional Covariance Estimation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eMethods for estimating sparse and large covariance matrices\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCovariance 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. \u003ci\u003eHigh-Dimensional Covariance Estimation \u003c\/i\u003eprovides 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.\u003c\/p\u003e \u003cp\u003eRecently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. \u003ci\u003eHigh-Dimensional Covariance Estimation\u003c\/i\u003e focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction,\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I MOTIVATION AND THE BASICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Least-Squares and Regularized Regression 4\u003c\/p\u003e \u003cp\u003e1.2 Lasso: Survival of the Bigger 6\u003c\/p\u003e \u003cp\u003e1.3 Thresholding the Sample Covariance Matrix 9\u003c\/p\u003e \u003cp\u003e1.4 Sparse PCA and Regression 10\u003c\/p\u003e \u003cp\u003e1.5 Graphical Models: Nodewise Regression 12\u003c\/p\u003e \u003cp\u003e1.6 Cholesky Decomposition and Regression 13\u003c\/p\u003e \u003cp\u003e1.7 The Bigger Picture: Latent Factor Models 14\u003c\/p\u003e \u003cp\u003e1.8 Further Reading 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Data, Sparsity and Regularization 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Data Matrix: Examples 22\u003c\/p\u003e \u003cp\u003e2.2 Shrinking the Sample Covariance Matrix 26\u003c\/p\u003e \u003cp\u003e2.3 Distribution of the Sample Eigenvalues 29\u003c\/p\u003e \u003cp\u003e2.4 Regularizing Covariances Like a Mean 30\u003c\/p\u003e \u003cp\u003e2.5 The Lasso Regression 32\u003c\/p\u003e \u003cp\u003e2.6 Lasso, Variable Selection and Prediction 36\u003c\/p\u003e \u003cp\u003e2.7 Lasso, Degrees of Freedom and BIC 37\u003c\/p\u003e \u003cp\u003e2.8 Some Alternatives to the Lasso Penalty 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Covariance Matrices 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definition and Basic Properties 46\u003c\/p\u003e \u003cp\u003e3.2 The Spectral Decomposition 49\u003c\/p\u003e \u003cp\u003e3.3 Structured Covariance Matrices 52\u003c\/p\u003e \u003cp\u003e3.4 Functions of a Covariance Matrix 55\u003c\/p\u003e \u003cp\u003e3.5 PCA: The Maximum Variance Property 59\u003c\/p\u003e \u003cp\u003e3.6 Modified Cholesky Decomposition 61\u003c\/p\u003e \u003cp\u003e3.7 Latent Factor Models 65\u003c\/p\u003e \u003cp\u003e3.8 GLM for Covariance Matrices 71\u003c\/p\u003e \u003cp\u003e3.9 GLM via the Cholesky Decomposition 73\u003c\/p\u003e \u003cp\u003e3.10 The GLM for Incomplete Longitudinal Data 76\u003c\/p\u003e \u003cp\u003e3.11 A Data Example: Fruit Fly Mortality Rate 81\u003c\/p\u003e \u003cp\u003e3.12 Simulating Random Correlation Matrices 85\u003c\/p\u003e \u003cp\u003e3.13 Bayesian Analysis of Covariance Matrices 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II COVARIANCE ESTIMATION: REGULARIZATION\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Regularizing the Eigenstructure 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Shrinking the Eigenvalues 96\u003c\/p\u003e \u003cp\u003e4.2 Regularizing The Eigenvectors 101\u003c\/p\u003e \u003cp\u003e4.3 A Duality between PCA and SVD 103\u003c\/p\u003e \u003cp\u003e4.4 Implementing Sparse PCA: A Data Example 106\u003c\/p\u003e \u003cp\u003e4.5 Sparse Singular Value Decomposition (SSVD) 108\u003c\/p\u003e \u003cp\u003e4.6 Consistency of PCA 109\u003c\/p\u003e \u003cp\u003e4.7 Principal Subspace Estimation 113\u003c\/p\u003e \u003cp\u003e4.8 Further Reading 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Sparse Gaussian Graphical Models 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Covariance Selection Models: Two Examples 116\u003c\/p\u003e \u003cp\u003e5.2 Regression Interpretation of Entries of ∑\u003csup\u003e-1\u003c\/sup\u003e 118\u003c\/p\u003e \u003cp\u003e5.3 Penalized Likelihood and Graphical Lasso 120\u003c\/p\u003e \u003cp\u003e5.4 Penalized Quasi-Likelihood Formulation 126\u003c\/p\u003e \u003cp\u003e5.5 Penalizing the Cholesky Factor 127\u003c\/p\u003e \u003cp\u003e5.6 Consistency and Sparsistency 130\u003c\/p\u003e \u003cp\u003e5.7 Joint Graphical Models 130\u003c\/p\u003e \u003cp\u003e5.8 Further Reading 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Banding, Tapering and Thresholding 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Banding the Sample Covariance Matrix 136\u003c\/p\u003e \u003cp\u003e6.2 Tapering the Sample Covariance Matrix 137\u003c\/p\u003e \u003cp\u003e6.3 Thresholding the Sample Covariance Matrix 138\u003c\/p\u003e \u003cp\u003e6.4 Low-Rank Plus Sparse Covariance Matrices 142\u003c\/p\u003e \u003cp\u003e6.5 Further Reading 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Multivariate Regression: Accounting for Correlation 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Multivariate Regression \u0026amp; LS Estimators 146\u003c\/p\u003e \u003cp\u003e7.2 Reduced Rank Regressions (RRR) 148\u003c\/p\u003e \u003cp\u003e7.3 Regularized Estimation of B 150\u003c\/p\u003e \u003cp\u003e7.4 Joint Regularization of (B;) 152\u003c\/p\u003e \u003cp\u003e7.5 Implementing MRCE: Data Examples 155\u003c\/p\u003e \u003cp\u003e7.5.1 Intraday Electricity Prices 155\u003c\/p\u003e \u003cp\u003e7.5.2 Predicting Asset Returns 158\u003c\/p\u003e \u003cp\u003e7.6 Further Reading 161\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406823629143,"sku":"9781118034293","price":71.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118034293.jpg?v=1730497238","url":"https:\/\/bookcurl.com\/products\/highdimensional-covariance-estimation-9781118034293","provider":"Book Curl","version":"1.0","type":"link"}