A local parameterization of orthogonal and semi-orthogonal matrices with applications

DOI10.1006/jmva.1998.1766zbMath0935.62069OpenAlexW2006273168MaRDI QIDQ1275415

Robert J. Boik

Publication date: 8 May 2000

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.1998.1766

zbMATH Keywords

eigenvalueseigenvectorssingular valuessingular vectorsprincipal componentscanonical correlationsunified approachasymptotic joint distributions

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic properties of parametric estimators (62F12) Factor analysis and principal components; correspondence analysis (62H25) Measures of association (correlation, canonical correlation, etc.) (62H20)

Related Items

Model-based principal components of correlation matrices ⋮ Asymptotic Expansion in Reduced Rank Regression Under Normality and Nonnormality ⋮ Approximations to the distribution of the sample correlation matrix ⋮ Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality ⋮ Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality ⋮ Principal components on coefficient of variation matrices ⋮ Asymptotic expansion of the sample correlation coefficient under nonnormality ⋮ Newton algorithms for analytic rotation: an implicit function approach ⋮ Accurate confidence intervals in regression analyses of non-normal data ⋮ Second-order accurate inference on eigenvalues of covariance and correlation matrices

Cites Work

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• Longitudinal data analysis using generalized linear models
• The commutation matrix: Some properties and applications
• The asymptotic variance matrix of the sample correlation matrix
• An inter-battery method of factor analysis
• Multivariate regression models for panel data
• The asymptotic covariance matrix of sample correlation coefficients under general conditions
• Asymptotic inference for eigenvectors
• Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations
• Unbiased estimation of fourth-order matrix moments
• Reduced-rank regression for the multivariate linear model
• Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices
• The asymptotic distribution of singular values with applications to canonical correlations and correspondence analysis
• The effects of nonnormality on tests for dimensionality in canonical correlation and MANOVA models
• Matrix derivatives with an application to an adaptive linear decision problem
• The likelihood ratio tests for the dimensionality of regression coefficients
• The comparison of interdependent correlations between optimal linear composites
• Quartic rotation criteria and algorithms
• ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS: NON-NORMAL CASE1
• TESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES
• A Method of Generating Best Asymptotically Normal Estimates with Application to the Estimation of Bacterial Densities
• A note on the consistency of estimators in the analysis of moment structures
• Estimating Equations for Parameters in Means and Covariances of Multivariate Discrete and Continuous Responses
• A Test for a Specific Principal Component of a Correlation Matrix
• The Analysis of Nonadditivity in Two-Way Analysis of Variance
• Reduced rank models for multiple time series
• Asymptotic expansions for the distributions of the sample roots under nonnormality
• Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations
• The asymptotic distribution of elements of a correlation matrix: Theory and application
• Testing the Rank and Definiteness of Estimated Matrices With Applications to Factor, State-Space and ARMA Models
• Asymptotic distribution of the sample roots for a nonnormal population
• The maximum-likelihood solution in inter-battery factor analysis
• Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis
• On the Asymptotic Properties of LDU-Based Tests of the Rank of a Matrix
• Mean and Covariance Structure Analysis: Theoretical and Practical Improvements
• Asymptotically distribution‐free methods for the analysis of covariance structures
• An Asymptotic Expansion for the Distribution of the Latent Roots of the Estimated Covariance Matrix
• Asymptotic Theory for Principal Component Analysis
• On the Sampling Theory of Roots of Determinantal Equations
• Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions