A Study On Some Theories In Small Area Estimation

Small area estimation has always been one of the difficult problems in the research of international sample survey theory. Although the Big Data Age has come, but the traditional sampling surveys will not disappear, and a growing number of sampling surveys require the effective estimation of each domain as well as the overall target variable so as to meet the demands of multi-level inference. In theory, this could be achieved by partitioning the domain which needs to be inferred as the sub-population of the level for stratified sampling. However, in reality, it is hard to achieve either for the high cost or for the small number of samples falling into each area to obtain an effective estimation of area target variable through conventional estimation method. Therefore, this paper makes a deep research on the design-based and model-based small area estimation theory and makes a breakthrough and development in small area estimation method.This paper makes a deep research mainly on the following issues:Firstly, the paper trails back systematically some sample designs aiming to improve the efficiency of area estimation home and abroad and divides them into homogenization sample distribution and area incremental according to the different effect on the number of samples. By comparing the different design ideas and principles of different methods, this paper comes up with their respective applicable occasions. On the base of systematic research of design-based small area estimation method home and abroad, this paper compares various estimators and points out their respective characteristics, mutual connections and further develop, on which the paper puts forward some asymptotic variance estimator expression, compares and summarizes their respective effects through numerical analysis.Secondly, this paper makes a research on the small area estimation method with double horizontal auxiliary information and brings in, on the base of traditional double level area estimation model, design-based calibration estimation method, and presents a new double level calibration estimators with model of auxiliary and deduces mean-square error of this estimator, which unifies the calibration estimator in the field of direct estimate field and indirect estimate field. This estimator can not only make full use of auxiliary information of small area level and cell level but also achieve an estimated accuracy better than BLUP estimator on some conditions and be more practical in practice.Last, this paper makes a research on the model-based Small area weighted estimation method in Honeycomb structure. Considering the special national conditions of our country, this paper analyzes the overall Honeycomb structure which is most popular in our government sampling investigation and establishes honeycomb Structure. Breaking down the limitations of recent model-based estimation theory, from the angle of weighting, this paper researches another estimation method, which, based on the model system, brings in design-based calibration constraints framework so as to put forward honeycomb-model-based area weighted estimator, which is particularly applicable to the methods of small area estimation of sample survey to meet the needs of multi-level inference in our country.