We propose a joint model for point estimates and their variances when observed variances may
contain bias. The bias in variances for groups of domains may be induced by an estimation procedure, such
the weight smoothing procedure of Beaumont (2008) to compute a domain point estimator. While the
weight-smoothed point estimator is more efficient than the original weighted survey estimator, its variance
estimation procedure requires truncations that induces bias in the domain variance estimator. The proposed
formulation generalizes the joint point estimator and variance models to explicitly parameterize a
multiplicative bias in observed variances under a nonparametric formulation 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 from the Current EmploymentStatistics survey and in simulations.