抽样调查中的小域估计方法研究

Small area estimation is a very important and difficult problem in survey sampling. It has been paid more and more attention by the researchers or statistican in survey sampling, and has been a hot topic in survey sampling or statistics. This project is designed to study the small area estimion in several important directions: Part 1 consider how to get the model-assisted rather than model-based small area estimaion; Part 2 focus on measuring the performance of small area estiamtors under the sampling design framework; Part 3 consider the adaptive small area estimation for areas with area-effects and without area-effects by LASSO method; Part 4 investigate the peanlized weighted least square method in general small area models and the choice of the penalty parameters for this method; Part 5 is an application research on agricultural survey, which we would make use of data from the satellite remote and survey sample data; Part 6 consider the effective estimation for demographic areas in our country. This project would extend the method research in small area estimation, and provide the application case for the practical statistican in our country.

在抽样调查中，小域估计是一个很重要也很棘手的问题，受到越来越多的抽样调查理论和实际工作者的重视，它已经成为抽样调查甚至统计学的热点研究领域。本项目将对小域估计中的若干重要问题进行深入研究，包括：（1）研究模型辅助而非基于模型的小域估计方法；（2）给出在抽样设计意义下小域估计的精度估计；（3）研究小域估计中的区别估计问题；（4）研究一般小域模型下的惩罚加权最小二乘方法及其惩罚参数的选取；（5）将农业的卫星遥感数据和实际调查数据相结合，研究小域估计在农业调查中的实际应用；（6）利用小域估计方法建立我国人口分区域的推算模型。本项目将进一步推动小域估计的理论与方法研究，将对解决我国抽样调查工作中的实际问题提供有力的新工具。

本项目完成了小区域估计的若干理论和应用问题。理论上，提出了逆惩罚概率加权方法，有效改进了之前方法的稳健性问题；应用上与国家统计局合作研究农作物播种面积的小区域估计问题，并取得了很好的应用成果。项目中后期，考虑到抽样技术在超大规模数据中的应用价值，项目中后期的工作重心转为抽样技术在大规模数据中的应用，并提出了有效的算法，取得了很好的研究成果。