  We consider parameter estimation of stochastic differential equations driven
by a Wiener process and a compound Poisson process as small noises. The goal is
to give a threshold-type quasi-likelihood estimator and show its consistency
and asymptotic normality under new asymptotics. One of the novelties of the
paper is that we give a new localization argument, which enables us to avoid
truncation in the contrast function that has been used in earlier works and to
deal with a wider class of jumps in threshold estimation than ever before.
