Abstract: We consider the estimation of cell probabilities in a two-way contingency table where the two-dimensional categorical data have nonrespondents imputed by using a conditional hot deck imputation method. Under simple random sampling, we establish asymptotic normality of cell probability estimators based on imputed data and derive explicitly the form of their asymptotic covariance matrix, which can be used for large sample inference. We also show that estimators based on imputed data are more efficient than those obtained by ignoring nonrespondents and re-weighting when the proportion of nonrespondents is large. The results are extended to stratified sampling, under imputation, within each stratum or across strata. Two types of asymptotics are studied under stratified sampling. One deals with the case of a fixed number of strata with large stratum sizes and the other deals with the situation of a large number of strata with small stratum sizes. Some simulation results are presented to study finite sample properties of the proposed procedures.
Key words and phrases: Estimation of cell probability, imputation across strata, re-weighting, stratified sampling.