Item nonresponse exists in most surveys and nonresponse rates are often appreciable. Nonresponse is ignorable if it is related to the observed data only; otherwise, it is nonignorable. Research for nonignorable nonresponse is far from complete. This investigator focuses on statistical estimation and inference in cross-sectional or longitudinal surveys with nonignorable nonresponse. Methods for deriving approximately unbiased and consistent survey estimators for parameters such as population totals and quantiles will be developed. In addition, the efficiency and robustness of estimators will also be studied. Effort will be made to study multivariate or longitudinal survey data, and problems with nonresponse in not only the main survey variables but also the covariates. This investigator will also study variance estimation for valid estimators, using methods such as linearization, substitution, replication or resampling such as the jackknife, the balanced half samples, the random groups, and the bootstrap.

Many statistical and government agencies collect data through surveys. In most of these surveys, there are typically people who do not respond to the survey, or give partial answers; such cases are called nonresponses. Often a nonresponse is related to the nonrespondent; for example, males under the age of twenty-five years may be more likely not to respond than older males. In this case, the statistical methodology is not well developed. The investigator plans to study methods for estimation and inference in the presence of nonresponse for various types of surveys. To increase the precision of estimators, effort will be made to use all observed data, to utilize auxilliary information, and to statistically model the nonresponse rate and/or distribution of the survey data. Methods of assessing the varibility of the derived estimators will also be studied. 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 methodology for handling noresponse in these survey agencies.

Project Report

My project focuses on missing-data problems in which the reason for missing values is related to the unobserved values. The primary goal is to derive valid estimators and inference methods for unknown population parameters. The main findings are that we can make valid inference by making use of auxilliary data to fill in the gap created by missing values. Methods developed includes imputation techniques, statistical model fitting under various assumptions, and adjustments in sampling weights. Results are derived under data sets in medical and health studies or surveys conducted by agencies such as the Census Bureau, the Bureau of Labor Statistics, and Statistics Canada, for example, the Current Population Survey and the Survey of Income and Program Participation (Census Bureau), the Current Employment Survey and the Employee Benefits Survey (Bureau of Labor Statistics), and Wisconsin Sleep Cohort Study for studying risk factors of very low birth weight infants and for atherogenesis in type I diabetes. Since research on the missing-data probblem, especially for multivariate or longitudinal data, is far from complete, my results will have many applications and encourage further studies in this area. Software are developed and will be available upon request. This project also provides training to nine Ph.D. students at University of Wisconsin-Madison.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Gabor J. Szekely
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University of Wisconsin Madison
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