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Modern Methods to Covariance Estimation : With High-Dimensional Data.
Methods for estimating sparse and large covariance matrices Covariance 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 sc...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.