Ranked Set Sampling (RSS) has been proved an economical way of estimating population characteristics. Various modifications based on RSS have been developed since the 1980s to improve precision. However, problems still persist. Little improvement has been made for nonparametric estimation. Decisions of sample sizes and necessary optimal designs of RSS in practice could be complicated, time-consuming, and unsuccessful after all. Imperfect ranking with potential subjective misjudgment or ranking with more than two characteristics also may hurt the efficiencies over other sampling methods. In this dissertation, we introduce a self-building system to better solve the above problems. In first part of the dissertation, we focus on exploring the properties in the Ranked Set Sampling, some of its many modifications and the Self building System for RSS. We use simulations to compare the performance of these methods under different distributions and ranking error assumptions. Our study indicates that the Self Building System for RSS has shown much better precision and robustness than other RSS-related modifications under most conditions for both nonparametric and parametric cases.
In the second part of the dissertation, we focus on statistical testing and regression analysis with concomitant variables of Self Building System for the RSS. The sign test is considered. The regression-type estimate of a population mean and the general regression analysis using Self Building System are discussed. The SBS procedure on multivariate sampling is also discussed. We also explore the applications in practice of the Self building system compared with RSS.