Variance estimation in the presence of nonrespondents and certainty strata

Business surveys often use a one-stage stratified simple random sampling without replacement design with some certainty strata. Although weight adjustment is typically applied for unit nonresponse, the variability due to nonresponse may be omitted in practice when estimating variances. This is problematic especially when there are certainty strata. We derive some variance estimators that are consistent when the number of sampled units in each weighting cell is large, using the jackknife, linearization, and modified jackknife methods. The derived variance estimators are first applied to empirical data from the Annual Capital Expenditures Survey conducted by the U.S. Census Bureau and are then examined in a simulation study.