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

Authors:
Leming Qu;Wotao Yin
Affiliations:
Department of Mathematics, Boise State University, Boise, ID 83725-1555, USA;Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
Venue:
Computational Statistics & Data Analysis
Year:
2012

Citing 6
Cited 1

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

Journal of Mathematical Imaging and Vision
Archimedean copula estimation using Bayesian splines smoothing techniques

Computational Statistics & Data Analysis
Linear B-spline copulas with applications to nonparametric estimation of copulas

Computational Statistics & Data Analysis
Thresholding methods to estimate copula density

Journal of Multivariate Analysis
The Split Bregman Method for L1-Regularized Problems

SIAM Journal on Imaging Sciences
Parametric Maximum Flow Algorithms for Fast Total Variation Minimization

SIAM Journal on Scientific Computing

Moment-independent regional sensitivity analysis: Application to an environmental model

Environmental Modelling & Software

Quantified Score

Hi-index	0.03

Visualization

Abstract

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.