  We investigate the validity of two resampling techniques when carrying out
inference on the underlying unknown copula using a recently proposed class of
smooth, possibly data-adaptive nonparametric estimators that contains empirical
Bernstein copulas (and thus the empirical beta copula). Following
\cite{KirSegTsu21}, the first resampling technique is based on drawing samples
from the smooth estimator and can only can be used in the case of independent
observations. The second technique is a smooth extension of the so-called
sequential dependent multiplier bootstrap and can thus be used in a time series
setting and, possibly, for change-point analysis. The two studied resampling
schemes are applied to confidence interval construction and the offline
detection of changes in the cross-sectional dependence of multivariate time
series, respectively. Monte Carlo experiments confirm the possible advantages
of such smooth inference procedures over their non-smooth counterparts. A
by-product of this work is the study of the weak consistency and finite-sample
performance of two classes of smooth estimators of the first-order partial
derivatives of a copula which can have applications in mean and quantile
regression.
