Efficiency, Sparsity and Validity in Analyzing Complex Survey Data

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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.**