Full bibliography

A small area procedure for a two-way table of proportions is developed, where the estimated proportions are from a complex survey. Estimation is difficult because the observed proportions do not have multinomial distributions, the observed proportions are correlated with estimated variances, benchmarking is required, and mean models are nonlinear. A predictor based on a nonlinear mixed model is specified for the proportions. No transformation of the observations is involved, and the estimation procedure gives predictions that are in the parameter space. A bootstrap estimator of the mean squared error of a benchmarked predictor is suggested and performed well in simulations. The procedure is applied to the proportions in the two-way table defined by occupations crossed with Canadian provinces. The direct estimators are from the Canadian Labour Force Survey (LFS), and the corresponding two-way table from the previous Canadian Census of Population provides auxiliary information. The application of the prediction procedure to the LFS data leads to gains in estimated mean squared errors relative to the direct estimators between approximately 30 percent and 80 percent. A comparison of the predictors to the Census 2006 proportions further supports the suggested procedures.