Generalized Variance Functions in Stratified Two-Stage Sampling
Abstract Generalized variance functions (GVF's) are used in a number of sample surveys as a convenient method of publishing sampling errors. The method consists of estimating the relative variance (relvariance) of an estimator of a total T by using a model with the form a + b/T. Using the prediction approach to finite population sampling, some asymptotic theory is presented for estimators of totals that are linear combinations of sample cluster means from stratified, two-stage cluster samples. One choice of GVF estimator is shown to be consistent under a particular class of prediction models. The theory is illustrated by an empirical study in which two-stage stratified samples are selected from a population of households. The prediction model is one in which units within a stratum have a common mean and variance, units in the same cluster are correlated but units in different clusters are not, and in which the common variance is a quadratic function of the common mean in a stratum. Bernoulli and Poisson r...