Bayesian Nonparametric Joint Model For Domain Point Estimates and Variances Under Biased Observed Variances

Abstract Government statistical agencies compose a population statistic for a given domain using a sample of units nested in that domain. Subsequent modeling of these domain survey estimates is often used to “borrow strength” across a dependence structure among the domains to improve estimation accuracy and efficiency. This paper focuses on models jointly defined for sample-based point estimates along with their sample-based estimates of variances. Bias may be present in the sample-based (observed) variances due to small sample sizes or the estimation procedure. We propose a new formulation that extends existing joint model formulations to allow for a multiplicative bias in observed variances. Our approach capitalizes on the unbiasedness property of point estimates. We utilize a nonparametric mixture construction that allows the data to discover distinct bias regimes. As a consequence of the better variance estimation, domain point estimates are more robustly estimated under a joint model for the domain point estimates and their associated variances. We compare the performances of alternative models in application to estimates of total employment from the Current Employment Statistics survey conducted by the US Bureau of Labor Statistics, and in simulations.