Linearization is one the very usual technique used in statistics to
approximate and estimate the variances. A large set of publications are
dedicated to methods of linearization including linearization of a function of
totals, of estimating equations of nonlinear functions of the observations.
Several techniques have been proposed. First we present a synthesis of these
different methods. Next we derive a new method consisting in differentiating by
the sampling indicators. This method can also be applied to calibrated
estimator. Finally, we show that this technique of linearization can also be
used to take the variance due to the nonresponse in reweighed of imputed
estimators into account.