  We investigate nonparametric drift estimation for multidimensional jump
diffusions based on continuous observations. The results are derived under
anisotropic smoothness assumptions and the estimators' performance is measured
in terms of the sup-norm loss. We present two different Nadaraya--Watson type
estimators, which are both shown to achieve the classical nonparametric rate of
convergence under varying assumptions on the jump measure. Fully data-driven
versions of both estimators are also introduced and shown to attain the same
rate of convergence. The results rely on novel uniform moment bounds for
empirical processes associated to the investigated jump diffusion, which are of
independent interest.
