  We consider the problem of delay estimation by the observations of the
solutions of several SDEs. It is known that the MLE for these models are
consistent and asymptotically normal, but the likelihood ratio functions are
not differentiable w.r.t. parameter and therefore numerical calculation of the
MLEs has certain difficulties. We propose One-step and Two-step MLE, whose
calculation has no such problems and provide estimator asymptotically
equivalent to the MLE. These constructions are realized in two or three steps.
First we construct preliminary estimators which are consistent and
asymptotically normal, but not asymptotically efficient. Then we use these
estimators and modified Fisher-score device to obtain One-step and Two-step
MLEs. We suppose that its numerical realization is much more simple. Stochastic
Pantograph equation is introduced and related statistical problems are
discussed.
