  Consider a process satisfying a stochastic differential equation with unknown
drift parameter, and suppose that discrete observations are given. It is known
that a simple least squares estimator (LSE) can be consistent, but numerically
unstable in the sense of large standard deviations under finite samples when
the noise process has jumps. We propose a filter to cut large shocks from data,
and construct the same LSE from data selected by the filter. The proposed
estimator can be asymptotically equivalent to the usual LSE, whose asymptotic
distribution strongly depends on the noise process. However, in numerical
study, it looked asymptotically normal in an example where filter was choosen
suitably, and the noise was a L\'evy process. We will try to justify this
phenomenon mathematically, under certain restricted assumptions.
