The Bootstrap Method in Survey Sampling

When no explicit variance formula is available and the calculations for Taylor linearization (cf., for instance, Wolter 2007, p. 230ff) are too cumbersome, so-called computer-intensive methods that use computer power instead of heavy calculations can be applied alternatively. One such procedure is the random group method (cf., for instance, Wolter 2007, Chap. 2). In this case, the sample drawn is divided into different nonoverlapping subsamples, called “random groups,” according to the original sampling design. After calculating the original estimator of the parameter under study in each of the groups, the variance of these estimators serves as the basis for extrapolation regarding the variance of the estimator in the original sample. The calculations are truly simple, but for obvious reasons are often inefficient for complex surveys because the construction of subgroups according to the original sampling design might be difficult.