Estimation under generalized sampling of cell proportions for contingency tables subject to marginal constraints

Under simple random (multinomial) sampling the problem of estimating cell proportions for a contingency table subject to marginal constraints has been well explored. We briefly review methods that have been considered; then we develop a general method, for more complicated sampling, which reflects the variance structure of the estimated cell proportions. For stratified and cluster sampling we compare our method against earlier methods for the 2×2 table and find it potentially advantageous.