Efficiency, Sparsity and Validity in Analyzing Complex Survey Data

大规模复杂调查在为政策制定者和公众以及公共卫生和社会科学研究等许多科学领域提供信息方面发挥着重要作用。这项研究通过四个广泛的研究项目解决了复杂调查数据分析的三个关键方面，即效率、稀疏性和有效性：(I)对无回答和缺失数据的有效半参数分数推算；(Ii)稀疏和高效的复制权重和用于方差估计的重采样方法；(Iii)用于有效和高效的基于设计的推理的贝叶斯经验似然方法；以及(Iv)用于大数据问题的有效抽样技术和有效的推理程序。 前两个项目致力于为丢失数据问题和方差估计技术这两个看似独立但相互纠缠的问题提供更有吸引力的战略和解决方案，这两个问题对于复杂的调查数据分析至关重要。第三个项目试图为具有复杂抽样设计特征的调查数据制定贝叶斯分析的一般框架和有用的方法，包括分层、分组和不等概率选择。主要目标是在基于设计的框架下开发具有有效频率解释的贝叶斯分析程序。最后一个项目试图抓住当前大数据问题的趋势，我们的潜在贡献是利用最初为有限人口问题开发的抽样技术，充分解决分析超大数据集的问题。 这项研究的预期结果将是高效、稀疏和有效的推理工具和战略，用于创建公共使用的微观调查数据文件，并进行复杂调查的统计分析。提案中概述的所有四个广泛项目都将涉及对硕士和博士研究生以及博士后研究员的培训。

Large scale complex surveys play an important role in providing information for policy makers and the general public as well as many scientific areas, such as public health and social science research. The proposed research addresses three critical aspects of complex survey data analysis, namely, efficiency, sparsity and validity, through four broad research projects: (i) Efficient semiparametric fractional imputation for nonresponses and missing data; (ii) Sparse and efficient replication weights and resampling methods for variance estimation; (iii) Bayesian empirical likelihood methods for valid and efficient design-based inferences; and (iv) Efficient sampling techniques and valid inference procedures for big data problems.  The first two projects strive to provide more attractive strategies and solutions to the two seemingly separate but entangled problems on missing data problems and variance estimation techniques, which are fundamentally important to complex survey data analysis. The third project attempts to develop a general framework and useful methodologies in Bayesian analysis for survey data with complex sampling design features involving stratification, clustering and unequal probability selection. The primary goal is to develop Bayesian analysis procedures with valid frequentist interpretation under the design-based framework. The last project tries to catch the current trend on big data problems, and our potential contribution is to adequately address issues in analyzing overly large data sets with sampling techniques originally developed for finite population problems.  The anticipated outcomes of this research will be efficient, sparse and valid inference tools and strategies for creating public use micro survey data files and for conducting statistical analysis of complex surveys. All four broad projects outlined in the proposal will involve training of graduate students at both master's and PhD levels and of postdoctoral fellows.