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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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 56; no. 2; pp. 384 - 398
Main Authors: Qu, Leming, Yin, Wotao
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.02.2012
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2011.07.016