Copula density estimation by total variation penalized likelihood with linear equality constraints

A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity an...

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Vydáno v:	Computational statistics & data analysis Ročník 56; číslo 2; s. 384 - 398
Hlavní autoři:	Qu, Leming, Yin, Wotao
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.02.2012 Elsevier
Edice:	Computational Statistics & Data Analysis
Témata:	Algorithms Augmented Lagrangian method Computational efficiency Computer simulation Copula density estimation Copula density estimation Total variation Maximum penalized likelihood estimation Augmented Lagrangian method Density Exact sciences and technology General topics Mathematics Matlab Maximum penalized likelihood estimation Multivariate analysis Nonparametric inference Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Probability density functions Sciences and techniques of general use Statistics Television Total variation Total variation Augmented Lagrangian method Copula density estimation Maximum penalized likelihood estimation Rank statistic Density estimation Optimization method Non parametric estimation Cross validation Random vector Multivariate analysis Penalty method Parametric method Linear constraint Marginal distribution Operator splitting Probability density function Ill posed problem Lagrangian method Symmetry Copulas Discriminant analysis Data analysis Lagrangian Numerical linear algebra Statistical estimation Algorithm Constrained optimization Regularization method Selection problem Numerical analysis Statistical computation Simulation Joint probability Equality constraint Maximum likelihood Regularization
ISSN:	0167-9473, 1872-7352
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Shrnutí:	A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting algorithm. It offers an order of magnitude improvement in computational efficiency over another TV-MPLE method without constraints solved by the log-barrier method for the second order cone program. A data-driven selection of the regularization parameter is through K-fold cross-validation (CV). Simulation and real data application show the effectiveness of the proposed approach. The MATLAB code implementing the methodology is available online.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0167-9473 1872-7352
DOI:	10.1016/j.csda.2011.07.016