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A Simulation Study of the Distribution of Fay’s Successive Difference Replication Variance Estimator
A Simulation Study of the Distribution of Fay’s Successive Difference Replication Variance Estimator
Abstract
Small area estimation with area level models requires variance estimates of the direct survey point estimates being modeled. Small are a direct variance estimates are likely to be unstable, suggesting modeling the variances to improve them. One aspect of such modeling would be to specify a probability distribution of the variance estimators. Here, we consider this for Fay’s successive difference replication variance estimator. More specifically, we examine via simulations whether the variance estimator could be assumed to approximately follow a scaled chi-squared distribution, and if so, with what value of the degrees of freedom? We study these questions for simple random samples of various sizes from various distributions (normal, Poisson, and Bernoulli). The motivation for this study comes from county modeling of ACS (American Community Survey) poverty estimates by the Census Bureau’s Small Area Income and Poverty Estimates program, as direct variances of the ACS poverty estimates are produced using Fay’s variance estimator.
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Page Last Revised - October 8, 2021
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