  A compound Poisson process whose parameters are all unknown is observed at
finitely many equispaced times. Nonparametric estimators of the jump and L\'evy
distributions are proposed and functional central limit theorems using the
uniform norm are proved for both under mild conditions. The limiting Gaussian
processes are identified and efficiency of the estimators is established.
Kernel estimators for the mass function, the intensity and the drift are also
proposed, their asymptotic properties including efficiency are analysed, and
joint asymptotic normality is shown. Inference tools such as confidence regions
and tests are briefly discussed.
