  When modeling the distribution of a multivariate continuous random vector
using the so-called \emph{copula approach}, it is not uncommon to have ties in
the coordinate samples of the available data because of rounding or lack of
measurement precision. Yet, the vast majority of existing inference procedures
on the underlying copula were both theoretically derived and practically
implemented under the assumption of no ties. Applying them nonetheless can lead
to strongly biased results. Some of the existing statistical tests can however
be adapted to provide meaningful results in the presence of ties. It is the
case of some tests of exchangeability, radial symmetry, extreme-value
dependence and goodness of fit. Detailed algorithms for computing approximate
p-values for the modified tests are provided and their finite-sample behaviors
are empirically investigated through extensive Monte Carlo experiments. An
illustration on a real-world insurance data set concludes the work.
