An implicit function approach to constrained optimization with applications to asymptotic expansions

DOI10.1016/j.jmva.2007.01.005zbMath1132.41320OpenAlexW1969313814MaRDI QIDQ2476147

Robert J. Boik

Publication date: 11 March 2008

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

Full work available at URL: https://doi.org/10.1016/j.jmva.2007.01.005

zbMATH Keywords

Lagrange multiplierssingular value decompositionEdgeworth expansionsfactor analysisTaylor series expansionsestimating functionsmatrix derivativesbordered Hessiansecond derivative testbordered determinantal criterion

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Asymptotic distribution theory in statistics (62E20) Parametric inference under constraints (62F30) Approximation with constraints (41A29) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items

Principal components on coefficient of variation matrices, Newton step methods for AD of an objective defined using implicit functions, Newton algorithms for analytic rotation: an implicit function approach, Asymptotic expansions in mean and covariance structure analysis

Cites Work

• The varimax criterion for analytic rotation in factor analysis
• Asymptotics of estimating equations under natural conditions.
• A note on Silvey's (1959) theorem
• Estimating equations with nuisance parameters: Theory and applications
• Standard errors for rotated factor loadings
• Standard errors for obliquely rotated factor loadings
• Matrix derivatives with an application to an adaptive linear decision problem
• Newton algorithms for analytic rotation: an implicit function approach
• A note on a Manova model applied to problems in growth curve
• Second-order accurate inference on eigenvalues of covariance and correlation matrices
• Quartic rotation criteria and algorithms
• The Lagrangian Multiplier Test
• Maximum-Likelihood Estimation of Parameters Subject to Restraints
• Some results on commutation matrices, with statistical applications
• GRADIENT METHODS FOR ANALYTIC ROTATION
• On direct product matrices
• SIMPLIFIED FORMULAE FOR STANDARD ERRORS IN MAXIMUM‐LIKELIHOOD FACTOR ANALYSIS
• Estimating equations, empirical likelihood and constraints on parameters
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