1984: a Comparison of Variance Estimators Using the Taylor Series Approximation

The selection of a variance estimator for large complex sample surveys is not straightforward. Most of the methods of variance estimstion for such surveys are b~sed upon some form of repeated subsampling. The random group, jackknife and balanced repeated replication methods differ primarily in the procedures for forming the subsamples. Previous comparative studies have been primarily empirical. One of our goals is to compare analytically the accuracy of these different subsample variance estimators. A first order Taylor series approximation is widely used in computing variances for complex surveys; however, the analytical properties of the random group, jackknife and hslanced repeated replication variance estimators are indistinguishable in their first order term. Koop (1968) hypothesized the underestimate of variance h~ found w~% due to neglecting terms of order i/n and i/n~. Sukhatme and Sukhatme (1970) suggested the use of a second order approximation. Our method of comparing these variance estimators is to include all the terms