Efficient Estimation of Parameters in Marginals in Semiparametric Multivariate Models

Associate Professor Artem Prokhorov, Concordia University, Montreal

8th Aug 2012  02:00 pm - Room 489 Merewether Building (H04)

Recent literature on semiparametric copula models focused on the situation when the marginals are speci
ed nonparametrically and the copula function is given a parametric form. For example, this setup is used in Chen, Fan and Tsyrennikov (2006) [Efficient Estimation of Semiparametric Multivariate Copula Models, JASA] who focus on
efficient estimation of copula parameters. We consider a reverse situation when the marginals are speci
ed parametrically and the copula function is modelled nonparametrically. This setting is no less relevant in applications. We use the method of sieve for efficient estimation of parameters in marginals, derive its asymptotic distribution and show that the estimator is semiparametrically
efficient. Simulations suggest that the sieve MLE can be up to 70% more efficient relative to QMLE depending on the strength of dependence between the marginals. An application using insurance company loss and expense data demonstrates empirical relevance of this setting.