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

Leming Qu and Wotao Yin

Computational Statistics & Data Analysis, 2012, vol. 56, issue 2, 384-398

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.

Keywords: Copula density estimation; Total variation; Maximum penalized likelihood estimation; Augmented Lagrangian method (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:2:p:384-398

DOI: 10.1016/j.csda.2011.07.016

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