On simplified estimators of unknown parameters with good asymptotic properties

A quite usual situation is considered when there exist estimators $\widehat\theta$ of unknown parameters $\theta$ having useful asymptotic properties which are difficult to compute: $\widehat\theta$ are roots of some known equations. A method is proposed that permits constructing simplified estimators asymptotically equivalent to $\widehat\theta$ based on any consistent estimators satisfying mild requirements. The method is a generalization of that proposed by Le Cam [1] in connection with a more special problem and it is used in particular for estimation of spectrum prameters of stationary stochastic processes with discrete and continuous time parameter.