05576nam 2200745Ia 450 991082871260332120240313225027.097811185736621118573668978111857361711185736179781118573655111857365X(CKB)2670000000360075(EBL)1204740(OCoLC)850164833(SSID)ssj0000887839(PQKBManifestationID)11459813(PQKBTitleCode)TC0000887839(PQKBWorkID)10846595(PQKB)10920269(MiAaPQ)EBC1204740(DLC) 2013012679(Au-PeEL)EBL1204740(CaPaEBR)ebr10716695(PPN)191470961(Perlego)1001604(EXLCZ)99267000000036007520130322d2013 uy 0engur|n|---|||||txtccrHigh-dimensional covariance estimation /Mohsen Pourahmadi1st ed.Hoboken, NJ Wileyc20131 online resource (208 p.)Wiley series in probability and statisticsDescription based upon print version of record.9781118034293 1118034295 Includes bibliographical references and index.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 Eigenvalues2.4 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 Data3.10.1 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 Reading5 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 Reading7 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"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"--Provided by publisher."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"--Provided by publisher.Wiley Series in Probability and StatisticsAnalysis of covarianceMultivariate analysisAnalysis of covariance.Multivariate analysis.519.5/38MAT029020bisacshPourahmadi Mohsen496526MiAaPQMiAaPQMiAaPQBOOK9910828712603321High-dimensional covariance estimation4036715UNINA