Fay's Method for Variance Estimation

Abstract

The standard balanced repeated replication (BRR) method of estimating variances involves dividing the sample in each stratum into half-samples, selecting a balanced set of half samples across all strata, re-computing the statistic of interest (generally nonlinear) on each selected half-sample, and taking the mean square difference of among the replicate estimates as the variance estimate. One problem that occasionally arises is that one or more replicate estimates will be undefined due to division by zero. This is particularly common when ratio estimation has been used with very small cell sizes. Robert Fay suggested a solution to this problem several years ago: Instead of increasing the weights of one half sample by 100% and decreasing the weights of the other half sample to zero, he recommended perturbing the weights by ± x%. In this article, his suggestion is evaluated with simulation techniques. It is shown to be useful when variance estimates are needed for both smooth and nonsmooth statistics or when there are very few degrees of freedom available for variance estimation. The paper also discusses further modifications to the technique that are useful for variance estimation when only one PSU is selected per stratum.