Variance Estimation

Calculation Methods

The two most popular classes in the calculation of correct variance estimates for complex sample surveys are replicate methods for variance estimation and Taylor series linearization methods. A third class of techniques that are sometimes used are generalized variance functions.

Replicate methods for variance compute multiple estimates in a systematic way and use the variability in these estimates to estimate the variance of the full-sample estimator. The simplest replicate method for variance is the method of random groups. The method of random groups was originally designed for interpenetrating samples or samples that are multiple repetitions (e.g., 10) of the same sampling strategy. Each of these repetitions is a random group, from which an estimate is derived. The overall estimator is the average of these estimates, and the estimated variance of the estimator is the sampling variance of the estimators. Of course, this technique can be used for any complex [Page 943]sample survey by separating the sample into sub-samples that are as equivalent as possible (e.g., by sorting by design variables and using systematic sampling to divide into random groups). This simplest of replicate methods for variance is simple enough to do by hand, but is not as robust as more modern replication-based methods that can now be easily calculated by computers.

Balanced repeated replication (BRR), also known as balanced half-samples, was originally conceived for use when two primary sampling units (PSUs) are selected from each stratum. A half-sample then consists of all cases from exactly one primary sampling unit from each stratum (with each weight doubled). Balanced half-sampling uses an orthogonal set of half-samples as specified by a Hadamard matrix. The variability of the half-sample estimates is taken as an estimate of the variance of the full-sample estimator.

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