Probability sample u-statistics: theory and applications for complex sample designs
Folsom, R. E. (1986, January). Probability sample u-statistics: theory and applications for complex sample designs. Presented at American Statistical Association Meeting, Section on Survey Research Methods, .
This paper summarizes research presented in my 1984 dissertation. The dissertation (Folsom, 1984) was devoted to the development of probabilitysample U-statistics theory. Applications of the theory were made to solve variance and variance component estimation problems for complex sample designs. In the domain of classical statistics where sampling from probability distributions is assumed, U-statistics theoryhas played an important role in the area of robust nonparametric inference. Variance components estimation has been one classical areawhere U-statistics theory has been applied to good advantage. By extending U-statistics theory into the realm of complex probabilitysamples, the unbiased Yates-Grundy-Sen variance estimator and associated variance component estimators are identified as degree 2 probability sample U-statistics. Considering the central role that variance and variance component estimates play in probability sample design andinference, the associated U-statistics theory provides a valuable new research and analysis tool for survey statistics