Point Estimation and Confidence Interval for Population Proportion under Triple Sampling Scheme

Population proportion is the percentage of the population that has a particular characteristic. The estimation for population proportion has broad applications in academic and industry fields such as insurance, banking, medical studies, bio-complexity and so on. Regarding an estimation procedure for population proportion, sampling scheme plays an important role. It directly decides the sampling space and the distribution of the sample statistics in interest, consequently, affects the results of estimations, from which people perceive and explore the characteristics of the population. Classical statistics in this area mostly focuses on a single random sample. Double sampling scheme has been increasingly gaining attention in the last three decades. Compared with a single sampling, a double sampling scheme can save resources by culling a population early in the sampling process while keeping the error rates under the nominal level in a hypothesis testing framework. The estimation process follows testing procedure as data cumulates. One possible further extension is to work with a triple sampling designed data. This thesis will focus on both point and confidence interval estimations for population proportions under a triple sampling scheme when the population following a binomial distribution. On the basis of introducing and reviewing methodologies for both single and double sampling schemes, this paper will explore how a triple sampling machinery works for the estimating process under a binomial distribution. The later part of this paper renders algorithms and simulation results for both double and triple sampling estimations, to evaluate the performance of this newly developed methodology. VI Acknowledgments In completing this graduate thesis, I am grateful for the supports and encouragements that many people have provided for me. First of all, I appreciate Dr. Yi Cheng, for her great amount of time and energy putting in helping make this thesis better. I appreciate for her great teaching too, which built for me an insight and necessary backgrounds for a long path. I thank the rest of my thesis committee members: Dr. Dean Alvis and Dr. Liguo Yu, their feedbacks helped to make this thesis better in many ways. I also thank Dr. Zhong Guan and Dr. Morteza Shafii-Mousavi for many of the academic backgrounds they helped me to build. All the professors mentioned above with whom I have taken two or more classes. Their meticulous teaching, patient tutoring and valuable advising provided for me a view, not only of my study at Indiana University South Bend, but …