Efficient Estimation of Semiparametric Multivariate Copula Models
Working Paper No. 04-W20
Xiaohong Chen, Yanqin Fan, and Victor Tsyrennikov
ABSTRACT [article]
We propose a sieve maximum likelihood (ML) estimation procedure for a
broad class of semiparametric multivariate distribution models. A joint
distribution in this class is characterized by a parametric copula
function evaluated at nonparametric marginal distributions. This class of
models has gained popularity in diverse fields due to a) its flexibility
in separately modeling the dependence structure and the marginal behaviors
of a multivariate random variable, and b) its circumvention of the "curse
of dimensionality" associated with purely nonparametric multivariate
distributions. We show that the plug-in sieve ML estimates of all smooth
functionals, including the finite dimensional copula parameters and the
unknown marginal distributions, are semiparametrically efficient; and that
their asymptotic variances can be estimated consistently. Moreover, prior
restrictions on the marginal distributions can be easily incorporated into
the sieve ML procedure to achieve further efficiency gains. Two such cases
are studied in the paper: (i) the marginal distributions are equal but
otherwise unspecifed, and (ii) some but not all marginal
distributions are parametric. Monte Carlo studies indicate that the sieve
ML estimates perform well in finite samples, especially so when prior
information on the marginal distributions is incorporated.
Keywords and Phrases: Multivariate copula, sieve maximum likelihood, semiparametric
efficiency
JEL Classification Number: C13, C14