Combining information from independent surveys, small area estimation of complex parameters, analysis of complex survey data

以概率抽样为基础的抽样调查被广泛用于就各种重要议题提供可靠的最新统计数据。变异性的量度（标准误差和置信区间）用于评估样本统计的质量。调查越来越多地被用于提供小区域的统计数据，例如县对贫困学龄儿童的估计，这是制定政策和方案、分配资金和营销决策所需要的。结合独立调查的信息（数据融合），以获得有效的估计和研究变量之间的关系，而不是在同一个调查中观察到的，受到了广泛的关注。调查数据被社会和健康科学家和其他人用来研究关系和测试感兴趣的假设，例如，加拿大国家公共卫生调查的纵向数据。我的研究计划将集中在所有当前感兴趣的上述主题。（a）我在小面积估算方面做了大量工作，我2003年出版的Wiley著作已成为研究人员和用户关于基于模型的方法的标准参考资料，即使在区域内样本规模很小的情况下，这种方法也能得出可靠的估算。我提议继续研究基于模型的方法，特别是使用现实模型和最佳估计方法，估计复杂的小区域参数，如世界银行在发展中国家使用的贫穷计量。(b)多水平模型通常用于分析多阶段抽样的数据，例如学校样本（水平2）和学校内的学生样本（水平1）。我计划研究我最近开发的一种新方法的理论特性和扩展，该方法可以导致有效的推论并提供统一的方法。(c)我最近的工作是把独立调查的信息结合起来，这为估计总数提供了有效的方法。扩展来处理更复杂的参数，如回归coefficeints，和丢失的数据将被研究。

Sample surveys, based on probability sampling, are widely used to provide reliable current statistics on a variety of important topics. Measures of variability (standard errors and confidence intervals) are used to assess the quality of the sample statistics. Surveys are increasingly being used to provide small area statistics, such as county estimates of poor school-age children, that are needed in formulating policies and programs, allocation of funds and marketing decisions. Combining information from independent surveys (data fusion) to obtain efficent estimates and study relationships between varaibles not all observed in the same survey has received much attention. Survey data are used by social and health scientists and others to study realtionships and to test hypotheses of interest, e.g, longitudinal data from the National Public Health Survey of Canada. My research program will focus on all the above topics of current interest. In particular, I plan to study the following problems among others:(a) I have done extensive work on small area estimation and my 2003 Wiley book has become a standard reference to researchers and users on model-based methods that can lead to reliable estimates even when the sample sizes are small within areas. I propose to continue my work on model-based methods, especially for estimating complex small area parameters such as poverty measures used by the World Bank in developing countries, using realistic models and optimal estimation methods. (b) Multi-level models are often used to analyse data from multistage sampling, e.g. sample of schools (level 2) and students (level 1) within schools. I plan to study the theoretical properties and extensions of a new method I have recently developed that leads to valid inferences and provides a unified approach. (c) My recent work on combining information from independent surveys provides efficient methods of estimating totals. Extensions to handle more complex parameters such as regression coefficeints, and missing data will be studied.