دانلود کتاب Shrinkage Estimation for Mean and Covariance Matrices (SpringerBriefs in Statistics)

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Preface
Contents
1 Decision-Theoretic Approach to Estimation
1.1 Decision-Theoretic Framework for Estimation
1.2 James-Stein\'s Shrinkage Estimator
1.3 Unbiased Risk Estimate and Stein\'s Identity
References
2 Matrix Algebra
2.1 Notation
2.2 Nonsingular Matrix and the Moore-Penrose Inverse
2.3 Kronecker Product and Vec Operator
2.4 Matrix Decompositions
References
3 Matrix-Variate Distributions
3.1 Preliminaries
3.1.1 The Multivariate Normal Distribution
3.1.2 Jacobians of Matrix Transformations
3.1.3 The Multivariate Gamma Function
3.2 The Matrix-Variate Normal Distribution
3.3 The Wishart Distribution
3.4 The Cholesky Decomposition of the Wishart Matrix
References
4 Multivariate Linear Model and Group Invariance
4.1 Multivariate Linear Model
4.2 A Canonical Form
4.3 Group Invariance
References
5 A Generalized Stein Identity and Matrix Differential Operators
5.1 Stein\'s Identity in Matrix-Variate Normal Distribution
5.2 Some Useful Results on Matrix Differential Operators
References
6 Estimation of the Mean Matrix
6.1 Introduction
6.2 The Unified Efron-Morris Type Estimators Including Singular Cases
6.2.1 Empirical Bayes Methods
6.2.2 The Unified Efron-Morris Type Estimator
6.3 A Unified Class of Matricial Shrinkage Estimators
6.4 Unbiased Risk Estimate
6.5 Examples for Specific Estimators
6.5.1 The Unified Efron-Morris Type Estimator
6.5.2 A Modified Stein-Type Estimator
6.5.3 Modified Efron-Morris Type Estimator
6.6 Related Topics
6.6.1 Positive-Part Rule Estimators
6.6.2 Shrinkage Estimation with a Loss Matrix
6.6.3 Application to a GMANOVA Model
6.6.4 Generalization in an Elliptically Contoured Model
References
7 Estimation of the Covariance Matrix
7.1 Introduction
7.2 Scale Invariant Estimators
7.3 Triangular Invariant Estimators and the James-Stein Estimator
7.3.1 The James-Stein Estimator
7.3.2 Improvement Using a Subgroup Invariance
7.4 Orthogonally Invariant Estimators
7.4.1 Class of Orthogonally Invariant Estimators
7.4.2 Unbiased Risk Estimate
7.4.3 Examples
7.5 Improvement Using Information on Mean Statistic
7.5.1 A Class of Estimators and Its Risk Function
7.5.2 Examples of Improved Estimators
7.5.3 Further Improvements with a Truncation Rule
7.6 Related Topics
7.6.1 Decomposition of the Estimation Problem
7.6.2 Decision-Theoretic Studies Under Quadratic Losses
7.6.3 Estimation of the Generalized Variance
7.6.4 Estimation of the Precision Matrix
References
Index