Statistics Seminar: Mohamad Khaled -- Estimation of copula models with discrete margins

Mohamad Khaled
Discipline of Operations Management & Econometrics
The University of Sydney Business School

Location: Carslaw 173 

Time: 2pm Friday, May 6, 2011 

Title: Estimation of copula models with discrete margins 

Abstract: Estimation of copula models with discrete margins is known to be difficult
beyond the bivariate case.  We show how this can be achieved by augmenting the
likelihood with uniform latent variables, and computing inference using the resulting
augmented posterior.  To evaluate this we propose two efficient Markov chain Monte Carlo
sampling schemes.  One generates the latent variables as a block using a
Metropolis-Hasting step with a proposal that is close to its target distribution.  Our
method applies to all parametric copulas where the conditional copula functions can be
evaluated, not just elliptical copulas as in previous Bayesian work.  Moreover, the
copula parameters can be estimated joint with any marginal parameters.  We establish the
effectiveness of the estimation method by modeling consumer behavior in online retail
using Archimedean and Gaussian copulas and by estimating 16 dimensional D-vine copulas
for a longitudinal model of usage of a bicycle path in the city of Melbourne,
Australia.  Finally, we extend our results and method to the case where some margins are
discrete and others continuous.  

The paper is a joint work with Professor Michael S.  Smith (Melbourne Business School).