Seminar za teoriju vjerojatnosti
Probability Seminar

2010./2011.:

Sažeci / Abstracts:

• Johan Segers, Université catholique de Louvain (joint work with Christian Genest, Université Laval): Inference on Copulas: When Ignorance is Bliss

  Consider the situation of a bivariate random sample from an unknown distribution with a completely unspecified copula but of which the margins are assumed to belong to parametric families. The interest is in the copula or a copula-related quantity (dependence measure). Copula estimators typically require the data to be transformed marginally to the standard uniform distribution via the probability integral transform. Since the marginal distributions are unknown, they have to be estimated. This can be done in two ways: nonparametrically using the empirical distribution functions or parametrically by plugging in estimators for the unknown marginal parameters. The first method gives rise to the empirical copula while the second method yields a kind of semiparametric copula estimator. Somewhat surprisingly, in all cases where analytical comparisons are feasible, the empirical copula has the smaller asymptotic variance. That is, even if the margins are known to be of some parametric form, it seems better to ignore this knowledge altogether and to proceed nonparametrically instead.

---

Prošli seminari / Past seminars:

• 2009./2010.
• 2008./2009.
• 2007./2008.