Imputation is a popular technique in handling nonresponse in surveys. This project focuses on the development of imputation methods that produce approximately unbiased and efficient survey estimators when imputed values are treated as observed data and standard methods are applied to compute the survey estimators. Various imputation methods will be studied, such as the nearest neighbor imputation, kernel nonparametric regression imputation, empirical likelihood, and techniques of handling measurement error. Emphasis will be placed on the study of multivariate survey variables and/or multivariate covariates, and problems with nonresponse in not only the main survey variables but also the covariates. 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, the random groups, and the bootstrap) that contains a re-imputation component to assess the variability caused by imputation. In particular, some shortcut replication methods that reduce the amount of computation will be investigated.
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. The research is supported by the Methodology, Measurement, and Statistics Program, the Statistics and Probability Program, and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.
