|
Abstract:
|
Small area estimation with area level models requires variance estimates of the direct survey point estimates being modeled. Small area 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 variance estimators-Fay's successive difference replication variance estimator. 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 for simple random samples of various sizes from various distributions (normal, Poisson, and Bernoulli). The motivation comes from county modeling of ACS poverty estimates by the Census Bureau's SAIPE program, as direct variances of the ACS poverty estimates are produced using Fay's estimator.
|
