In surveys aimed at estimating the size of a population, there often are individuals in the target population who are unaccounted for in the survey. If such undercounts are not adjusted for, a misrepresentation of the population results. This has led to the development of multiple system surveys, often called capture-recapture surveys. Estimation for such surveys requires a number of restrictive assumptions on unobserved characteristics of the population being studied, and it is of interest to develop estimation and inference methods that are less sensitive to those assumptions. This project intends to relax several of these fundamental assumptions with a unified nonparametric framework based on the kernel regression estimator. A novel nonparametric estimator of the capture probability will be developed that admits both continuous and categorical variables, and can be used in an unequal-probability survey context. This estimator then will be applied in several areas of population size estimation, including in the adjustment of existing population estimators, the correction for frame errors, and in model and assumption checking.
Estimating the magnitude of a population is an important goal of many surveys, including national censuses, surveys of special populations, and many wildlife studies. A large and important application is the U.S. Decennial Census, which is designed to provide accurate counts on the total and subtotal of various groups of the U.S. population. Population size estimates from such censuses and studies are all subject to potential undercount and, more rarely, overcount. For example, analysis of U.S. Census data shows that certain sections of the U.S. population are much harder to enumerate than the rest of the population. The goal of this research is to produce robust and efficient population size estimators that adjust for the presence of undercounts and other types of survey errors, and are appropriate for a wide range of survey settings. By combining methods from several areas of statistics, this research ultimately will contribute to the development of new statistical methodology that is directly relevant to on-going work at federal statistical agencies. The research is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.
