A Simple Method for Approximating the Variance of a Complicated Estimate

A method often used for computing the variance of a complicated sample estimate is to first apply the Taylor approximation to reduce non-linear forms of the variables to linear form. This article shows the useful results which can be obtained by merely reversing the order between selection units and component variables in this linear expression. The method is completely general (assuming that the samples are large enough to justify using the Taylor approximation) involving no restrictions on (a) the form of the estimate, (b) the number of random variables involved in the estimate, (c) the type, complexity or number of the sample designs involved in the estimate.