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Matrix Differential Calculus with Applications in Statistics and Econometrics
Jan R. Magnus,Heinz Neudecker +1 more
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In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.Abstract:
Preface MATRICES: Basic Properties of Vectors and Matrices Kronecker Products, the Vec-Operator and the Moore- Penrose Inverse Miscellaneous Matrix Results DIFFERENTIALS: THE THEORY: Mathematical Preliminaries Differentials and Differentiability The Second Differential Static Optimization DIFFERENTIALS: THE PRACTICE: Some Important Differentials First- Order Differentials and Jacobian Matrices Second-Order Differentials and Hessian Matrices INEQUALITIES: Inequalities THE LINEAR MODEL: Statistical Preliminaries The Linear Regression Model Further Topics in the Linear Model APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: Maximum Likelihood Estimation Simultaneous Equations Topics in Psychometrics Subject Index Bibliography.read more
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A Scaled Difference Chi-square Test Statistic for Moment Structure Analysis
Albert Satorra,Peter M. Bentler +1 more
TL;DR: In this paper, Satorra and Bentler's scaling corrections are used to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data.
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Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances
TL;DR: In this paper, the authors study the properties of the quasi-maximum likelihood estimator and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood is maximized but the assumption of normality is violated.
Book
Optimization Algorithms on Matrix Manifolds
TL;DR: Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis and will be of interest to applied mathematicians, engineers, and computer scientists.
Posted Content
Online Learning for Matrix Factorization and Sparse Coding
TL;DR: A new online optimization algorithm is proposed, based on stochastic approximations, which scales up gracefully to large data sets with millions of training samples, and extends naturally to various matrix factorization formulations, making it suitable for a wide range of learning problems.
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Matrix Algebra From a Statistician's Perspective.
TL;DR: In this article, the authors consider the minimization of a second-degree polynomial subject to linear constraints and show that the Moore-Penrose inverse can be reduced to a linear transformation.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
The varimax criterion for analytic rotation in factor analysis
TL;DR: In this article, an analytic criterion for rotation is defined and the scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed, and a computational outline for the orthogonal normal varimax is appended.
Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.