  Asymptotic theory for approximate martingale estimating functions is
generalised to diffusions with finite-activity jumps, when the sampling
frequency and terminal sampling time go to infinity. Rate optimality and
efficiency are of particular concern. Under mild assumptions, it is shown that
estimators of drift, diffusion, and jump parameters are consistent and
asymptotically normal, as well as rate-optimal for the drift and jump
parameters. Additional conditions are derived, which ensure rate-optimality for
the diffusion parameter as well as efficiency for all parameters. The findings
indicate a potentially fruitful direction for the further development of
estimation for jump-diffusions.
