The Research Of Multi-objective Stratified Sampling Method And Its Application

The sampling survey is an effective tool to reflect the overall social situation, so it requires the sampling's objective to estimate population parameter from all aspects. And multi-objective sampling theory is urgently needed for the sampling practice. Multi-objective stratified sampling method plays a very good role to improve sampling accuracy, but there is not mature theoretical method in this aspect. So this article attempts to present some research on multi-objective stratified sampling.In chapter one, author gives the topics background, domestic and international research status, theoretical significance and practical significance, and the main contents of the article. In chapter two, we explain the concept and stratify the range of multi-dimensional variables by using the probability method. In addition, we Construct sampling statistics, and prove it's the good properties. Finally, we prove the conclusion by replacement and without replacement sampling. In chapter three, we firstly talk about how to stratify multi-target sample by clustering analysis method. Secondly, this paper presents a new method of classification level, whose name is method of rectangular region, and constructs a sample statistic and proves its sampling error is less than simple random sampling's sampling error. Finally, we prove the conclusion by replacement and without replacement sampling. Chapter four uses the historical data to simulate a sampling and verifies the conclusions of this paper. Chapter five summarizes the innovations and research prospects.We have some ideas maybe new, but definitely they need to be ameliorated. They are expatiated as the following: Firstly, we stratify the multi-objective population by using the probability method. Secondly, this paper presents a new method of classification level, whose name is method of rectangular region. Thirdly, we obtain the comparison conclusion of multi-objective stratified sampling and simple random sampling error. Finally, this paper enriches Cochran"s conclusion.