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High-dimensional covariance estimation [[electronic resource] /] / Mohsen Pourahmadi
| High-dimensional covariance estimation [[electronic resource] /] / Mohsen Pourahmadi |
| Autore | Pourahmadi Mohsen |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2013 |
| Descrizione fisica | 1 online resource (208 p.) |
| Disciplina | 519.5/38 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Analysis of covariance
Multivariate analysis |
| ISBN |
1-118-57366-8
1-118-57361-7 1-118-57365-X |
| Classificazione | MAT029020 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910141572603321 |
Pourahmadi Mohsen
|
||
| Hoboken, NJ, : Wiley, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
High-dimensional covariance estimation / / Mohsen Pourahmadi
| High-dimensional covariance estimation / / Mohsen Pourahmadi |
| Autore | Pourahmadi Mohsen |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2013 |
| Descrizione fisica | 1 online resource (208 p.) |
| Disciplina | 519.5/38 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Analysis of covariance
Multivariate analysis |
| ISBN |
1-118-57366-8
1-118-57361-7 1-118-57365-X |
| Classificazione | MAT029020 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910828712603321 |
|
Pourahmadi Mohsen
|
||
| Hoboken, NJ, : Wiley, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||