Imputation Methodology for Complex Survey Problems

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The proposed research focuses on imputation and variance estimation after imputation for survey data with nonresponse. Marginal imputation (such as random hot deck imputation, nearest neighbor imputation, and random regression imputation) will be studied for the purpose of estimating population totals and quantiles. The investigator will also study joint imputation (for estimating parameters such as the coefficients of correlation or the cell probabilities in a contingency table) and imputation under nonignorable response. For each imputation method, variance estimation that takes nonresponse and imputation into account will be studied, using a direct derivation approach or a replication method such as the jackknife, the balanced half samples, and the bootstrap.Many statistics and government agencies collect data through surveys. Most surveys have nonresponse. Item nonresponse occurs when some sampled units cooperate in the survey but fail to provide answers to some questions. Imputation techniques, which insert values for nonrespondents, are commonly used compensation procedures for item nonresponse. In some cases, when auxiliary information is properly used, imputation increases statistical accuracy. An essential requirement for an imputation method is that one can obtain unbiased (or approximately unbiased) survey estimators by treating the imputed values as observed data and using the standard estimation formulas designed for the case of no nonresponse. This requires developments on imputation methodology and statistical analysis procedures to take nonresponse and imputation into account. Since most of the proposed research topics are motivated by problems in survey agencies such as the Census Bureau, the Bureau of Labor Statistics, Westat, and Statistics Canada, results obtained from the proposed research will have significant impacts on the imputation and variance estimation methodology for these survey agencies.