  In this paper we establish the uniform in bandwidth consistency for the
transformation kernel estimator of copulas introduced in [Omelka et al.(2009)].
To this end, we first prove a uniform in bandwidth law of the iterated
logarithm for the maximal deviation of this estimator from its expectation. We
then show that, as n goes to infinity, the bias of the estimator converges to
zero uniformly in the bandwidth h, varying over a suitable interval. A
practical method of selecting the optimal bandwidth is also presented. Finally,
we make conclusive simulation experiments showing the performance of the
estimator in finite samples.
