Further Simulation Results on the Distribution of Some Survey Variance Estimators

• Activity Number: 527
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Elizabeth T. Huang*+ and William R. Bell
• Companies: U.S. Census Bureau and U.S. Census Bureau
• Keywords: sampling variance ; degrees of freedom ; chi-squared distribution ; sample size

Abstract

A relatively new aspect to small area estimation with area level models involves modeling direct survey variances for small areas to improve them. Here, as one aspect of this, we consider the distribution of some survey variance estimators- linearization,Fay's successive difference replication variance estimator, the jackknife, and the random group. We use simulations to examine whether the variance estimators might be assumed to approximately follow a scaled chi-squared distribution, and if so, with what value of the degrees of freedom? We do this for variances of estimated proportions from simple random samples of various sizes, with data generated from various distributions (Poisson, and Bernoulli),and from American Community Survey data. This builds on previous work where we considered Fay's successive difference replication variance estimator for means from simple random samples