Key Words: Balanced repeated replication with Fay factors; Influence function;

estimator stability. In establishment surveys, sample designs often include stratification by the size of the establishment, with large establishments included in strata that have nontrivial sample fractions. For these designs, development and evaluation of appropriate variance estimators generally involve trade-offs among several factors, including the following. (1) The intended use of the variance estimator, e.g., for formal inference or for construction of weights in a weighted-least-squares procedure. (2) The extent, if any, to which one mus