  We consider M-estimation problems, where the target value is determined using
a minimizer of an expected functional of a Levy process. With discrete
observations from the Levy process, we can produce a "quasi-path" by shuffling
increments of the Levy process, we call it a quasi-process. Under a suitable
sampling scheme, a quasi-process can converge weakly to the true process
according to the properties of the stationary and independent increments. Using
this resampling technique, we can estimate objective functionals similar to
those estimated using the Monte Carlo simulations, and it is available as a
contrast function. The M-estimator based on these quasi-processes can be
consistent and asymptotically normal.
