Result: Miscellanea Positive definite estimators of large covariance matrices
Title:
Miscellanea Positive definite estimators of large covariance matrices
Authors:
Source:
Biometrika. 99(3):733-740
Publisher Information:
Oxford: Oxford University Press, 2012.
Publication Year:
2012
Physical Description:
print, 1/2 p
Original Material:
INIST-CNRS
Subject Terms:
General biology, Biologie générale, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Probabilités et statistiques, Probability and statistics, Statistiques, Statistics, Généralités, General topics, Applications, Biologie, psychologie, sciences sociales, Biology, psychology, social sciences, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Accélération convergence, Convergence acceleration, Aceleración convergencia, Algorithme, Algorithm, Algoritmo, Algèbre linéaire numérique, Numerical linear algebra, Algebra lineal numérica, Analyse discriminante, Discriminant analysis, Análisis discriminante, Analyse multivariable, Multivariate analysis, Análisis multivariable, Analyse numérique, Numerical analysis, Análisis numérico, Biométrie, Biometrics, Biometría, Calcul variationnel, Variational calculus, Cálculo de variaciones, Fonction logarithmique, Logarithmic function, Función logarítmica, Matrice covariance, Covariance matrix, Matriz covariancia, Matrice creuse, Sparse matrix, Matriz dispersa, Matrice définie positive, Positive definite matrix, Matriz definida positiva, Méthode optimisation, Optimization method, Método optimización, Méthode pénalité, Penalty method, Método penalidad, Méthode statistique, Statistical method, Método estadístico, Optimisation, Optimization, Optimización, Programmation mathématique, Mathematical programming, Programación matemática, Simulation, Simulación, Sondage statistique, Sample survey, Ecuesta estadística, Taille échantillon, Sample size, Tamaño muestra, Taux convergence, Convergence rate, Relación convergencia, Théorie échantillonnage, Sampling theory, Teoría muestreo, 49XX, 62D05, 62H30, 65B99, 65F50, 65K10, 65Kxx, Classification automatique(statistiques), Barrier function, Classification, Convex optimization, High-dimensional data, Sparsity
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, United States
ISSN:
0006-3444
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.26308781
Database:
PASCAL Archive
Further Information
Using convex optimization, we construct a sparse estimator of the covariance matrix that is positive definite and performs well in high-dimensional settings. A lasso-type penalty is used to encourage sparsity and a logarithmic barrier function is used to enforce positive definiteness. Consistency and convergence rate bounds are established as both the number of variables and sample size diverge. An efficient computational algorithm is developed and the merits of the approach are illustrated with simulations and a speech signal classification example.