High-dimensional covariance estimation [[electronic resource] /] / Mohsen Pourahmadi

• Autore: Pourahmadi Mohsen
• Pubblicazione: Hoboken, NJ, : Wiley, c2013
• Descrizione fisica: 1 online resource (208 p.)
• Disciplina: 519.5/38
• Soggetto topico: Analysis of covariance; Multivariate analysis
• Classificazione: MAT029020
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: HIGH-DIMENSIONAL COVARIANCE ESTIMATION; CONTENTS; PREFACE; I MOTIVATION AND THE BASICS; 1 INTRODUCTION; 1.1 Least Squares and Regularized Regression; 1.2 Lasso: Survival of the Bigger; 1.3 Thresholding the Sample Covariance Matrix; 1.4 Sparse PCA and Regression; 1.5 Graphical Models: Nodewise Regression; 1.6 Cholesky Decomposition and Regression; 1.7 The Bigger Picture: Latent Factor Models; 1.8 Further Reading; 2 DATA, SPARSITY, AND REGULARIZATION; 2.1 Data Matrix: Examples; 2.2 Shrinking the Sample Covariance Matrix; 2.3 Distribution of the Sample Eigenvalues ; 2.4 Regularizing Covariances Like a Mean2.5 The Lasso Regression; 2.6 Lasso: Variable Selection and Prediction; 2.7 Lasso: Degrees of Freedom and BIC; 2.8 Some Alternatives to the Lasso Penalty; 3 COVARIANCE MATRICES; 3.1 Definition and Basic Properties; 3.2 The Spectral Decomposition; 3.3 Structured Covariance Matrices; 3.4 Functions of a Covariance Matrix; 3.5 PCA: The Maximum Variance Property; 3.6 Modified Cholesky Decomposition; 3.7 Latent Factor Models; 3.8 GLM for Covariance Matrices; 3.9 GLM via the Cholesky Decomposition; 3.10 GLM for Incomplete Longitudinal Data ; 3.10.1 The Incoherency Problem in Incomplete Longitudinal Data3.10.2 The Incomplete Data and The EM Algorithm; 3.11 A Data Example: Fruit Fly Mortality Rate; 3.12 Simulating Random Correlation Matrices; 3.13 Bayesian Analysis of Covariance Matrices; II COVARIANCE ESTIMATION: REGULARIZATION; 4 REGULARIZING THE EIGENSTRUCTURE; 4.1 Shrinking the Eigenvalues; 4.2 Regularizing The Eigenvectors; 4.3 A Duality between PCA and SVD; 4.4 Implementing Sparse PCA: A Data Example; 4.5 Sparse Singular Value Decomposition (SSVD); 4.6 Consistency of PCA; 4.7 Principal Subspace Estimation; 4.8 Further Reading ; 5 SPARSE GAUSSIAN GRAPHICAL MODELS5.1 Covariance Selection Models: Two Examples; 5.2 Regression Interpretation of Entries of Σ-1; 5.3 Penalized Likelihood and Graphical Lasso; 5.4 Penalized Quasi-Likelihood Formulation; 5.5 Penalizing the Cholesky Factor; 5.6 Consistency and Sparsistency; 5.7 Joint Graphical Models; 5.8 Further Reading; 6 BANDING, TAPERING, AND THRESHOLDING; 6.1 Banding the Sample Covariance Matrix; 6.2 Tapering the Sample Covariance Matrix; 6.3 Thresholding the Sample Covariance Matrix; 6.4 Low-Rank Plus Sparse Covariance Matrices; 6.5 Further Reading ; 7 MULTIVARIATE REGRESSION: ACCOUNTING FOR CORRELATION7.1 Multivariate Regression and LS Estimators; 7.2 Reduced Rank Regressions (RRR); 7.3 Regularized Estimation of B; 7.4 Joint Regularization of (B, Ω); 7.5 Implementing MRCE: Data Examples; 7.5.1 Intraday Electricity Prices; 7.5.2 Predicting Asset Returns; 7.6 Further Reading; BIBLIOGRAPHY; INDEX; WILEY SERIES IN PROBABILITY AND STATISTICS
• Sommario/riassunto: "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"--; "The aim of this book is to provide computationally feasible and statistically efficient methods for estimating sparse and large covariance matrices of high-dimensional data"--
• Titolo autorizzato: High-dimensional covariance estimation
• ISBN: 1-118-57366-8; 1-118-57361-7; 1-118-57365-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910141572603321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley Series in Probability and Statistics