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High-Dimensional Covariance Estimation: With High-Dimensional Data [Kõva köide]

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  • Formaat: Hardback, 208 pages, kõrgus x laius x paksus: 246x163x17 mm, kaal: 431 g, Charts: 50 B&W, 0 Color; Graphs: 50 B&W, 0 Color
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 09-Aug-2013
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118034295
  • ISBN-13: 9781118034293
Teised raamatud teemal:
High-Dimensional Covariance Estimation: With High-Dimensional DataSuurem pilt
  • Formaat: Hardback, 208 pages, kõrgus x laius x paksus: 246x163x17 mm, kaal: 431 g, Charts: 50 B&W, 0 Color; Graphs: 50 B&W, 0 Color
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 09-Aug-2013
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118034295
  • ISBN-13: 9781118034293
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781118034293.html
Märksõnad:
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 sciences. High-Dimensional Covariance Estimation provides 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.

Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task.

High-Dimensional Covariance Estimation features chapters on:





Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression

The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Preface ix
I Motivation And The Basics
1 Introduction
3(18)
1.1 Least Squares and Regularized Regression
4(2)
1.2 Lasso: Survival of the Bigger
6(3)
1.3 Thresholding the Sample Covariance Matrix
9(1)
1.4 Sparse PCA and Regression
10(3)
1.5 Graphical Models: Nodewise Regression
13(1)
1.6 Cholesky Decomposition and Regression
13(2)
1.7 The Bigger Picture: Latent Factor Models
15(2)
1.8 Further Reading
17(4)
2 Data, Sparsity, And Regularization
21(24)
2.1 Data Matrix: Examples
22(4)
2.2 Shrinking the Sample Covariance Matrix
26(3)
2.3 Distribution of the Sample Eigenvalues
29(1)
2.4 Regularizing Covariances Like a Mean
30(2)
2.5 The Lasso Regression
32(4)
2.6 Lasso: Variable Selection and Prediction
36(1)
2.7 Lasso: Degrees of Freedom and BIC
37(1)
2.8 Some Alternatives to the Lasso Penalty
38(7)
3 Covariance Matrices
45(54)
3.1 Definition and Basic Properties
45(4)
3.2 The Spectral Decomposition
49(4)
3.3 Structured Covariance Matrices
53(3)
3.4 Functions of a Covariance Matrix
56(5)
3.5 PCA: The Maximum Variance Property
61(2)
3.6 Modified Cholesky Decomposition
63(4)
3.7 Latent Factor Models
67(6)
3.8 GLM for Covariance Matrices
73(3)
3.9 GLM via the Cholesky Decomposition
76(3)
3.10 GLM for Incomplete Longitudinal Data
79(5)
3.10.1 The Incoherency Problem in Incomplete Longitudinal Data
79(2)
3.10.2 The Incomplete Data and The EM Algorithm
81(3)
3.11 A Data Example: Fruit Fly Mortality Rate
84(5)
3.12 Simulating Random Correlation Matrices
89(2)
3.13 Bayesian Analysis of Covariance Matrices
91(8)
II Covariance Estimation: Regularization
4 Regularizing The Eigenstructure
99(22)
4.1 Shrinking the Eigenvalues
100(5)
4.2 Regularizing The Eigenvectors
105(2)
4.3 A Duality between PCA and SVD
107(3)
4.4 Implementing Sparse PCA: A Data Example
110(2)
4.5 Sparse Singular Value Decomposition (SSVD)
112(2)
4.6 Consistency of PCA
114(4)
4.7 Principal Subspace Estimation
118(1)
4.8 Further Reading
119(2)
5 Sparse Gaussian Graphical Models
121(20)
5.1 Covariance Selection Models: Two Examples
122(2)
5.2 Regression Interpretation of Entries of Σ-1
124(2)
5.3 Penalized Likelihood and Graphical Lasso
126(5)
5.4 Penalized Quasi-Likelihood Formulation
131(1)
5.5 Penalizing the Cholesky Factor
132(4)
5.6 Consistency and Sparsistency
136(1)
5.7 Joint Graphical Models
137(2)
5.8 Further Reading
139(2)
6 Banding, Tapering, And Thresholding
141(12)
6.1 Banding the Sample Covariance Matrix
142(2)
6.2 Tapering the Sample Covariance Matrix
144(1)
6.3 Thresholding the Sample Covariance Matrix
145(4)
6.4 Low-Rank Plus Sparse Covariance Matrices
149(1)
6.5 Further Reading
150(3)
7 Multivariate Regression: Accounting For Correlation
153(18)
7.1 Multivariate Regression and LS Estimators
154(2)
7.2 Reduced Rank Regressions (RRR)
156(2)
7.3 Regularized Estimation of B
158(2)
7.4 Joint Regularization of (B, Ω)
160(3)
7.5 Implementing MRCE: Data Examples
163(4)
7.5.1 Intraday Electricity Prices
163(2)
7.5.2 Predicting Asset Returns
165(2)
7.6 Further Reading
167(4)
Bibliography 171(10)
Index 181
MOHSEN POURAHMADI, PhD, is Professor of Statistics at Texas A&M University. He is an elected member of the International Statistical Institute, a Fellow of the American Statistical Association, and a member of the American Mathematical Society. Dr. Pourahmadi is the author of Foundations of Time Series Analysis and Prediction Theory, also published by Wiley.