Variance estimation for complex statistics and estimators: Linearization and residual techniques

Jean-Claude Deville shows how to use simple tools to calculate the variance of a complex estimator using a linearization technique. The process is that of a software used at INSEE for estimation of the variance of a complex estimator. It gives a way of computing the variance of a total estimated by the simple expansion estimator. In the case of a complex statistic, the process uses a derived variable that reduces the computations to those of the simple expansion estimator. Multiple examples are given to illustrate the process.