The proposed research focuses on imputation and variance estimation after imputation for survey data with nonresponse. The investigator will study different models that relate auxiliary variables and the variable to be imputed (e.g., parametric, non-parametric, and semi-parametric models); different response mechanisms (ignorable or non-ignorable); various imputation techniques (e.g., regression, nearest neighbor, and random imputation); different types of estimators (e.g., sample mean and sample quantiles); and different types of data (e.g., cross-sectional, clustered, or longitudinal data). The investigator will also study a pseudo empirical likelihood imputation method that provides more efficient survey estimators than other imputation methods. 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) that contains a re-imputation component to assess the variability caused by imputation.
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 and their variability 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.
