Robust inference for complex survey data

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Complex surveys play an important role in providing information for policy makers and the general public as well as many scientific in other areas, such as public health and social science research. Since the 1950's, National Statistical Offices (NSO) have been using probability sampling methods and inferences were conducted with respect to the so--called design--based framework, which can be viewed as a model--free framework. In the last decade, the role of models in survey sampling has become more and more important. This shift of paradigm can be explained by three main factors: (i) decreasing response rates; (ii) high data collection costs and (iii) the proliferation of non--probability data sources that include web survey panels and satellite information. The primary objective of this project is to propose new strategies for addressing these challenges through four broad projects: (a) Multiply robust estimation procedures in the context of sample matching and propensity score estimation. (b) Multiply robust imputation procedures for complex parameters including distribution function and quantiles. (c) Outlier--resistant methods for small area estimation and multiply robust estimators of finite population means and average treatment effects; (d) Development of strategies for chasing nonrespondents and selective editing using the conditional bias of a unit. Multiply robust procedures make use of multiple outcome regression models and/or multiple propensity score models. A procedure is said to be multiply robust if it remains consistent when all but one of the models are misspecified. The first two projects strive to provide attractive strategies and solutions to the two seemingly separate but entangled problems on missing data problems and statistical matching. The third project attempts to develop estimation procedures that exhibit low mean square errors in the presence of influential units, which are common in business surveys. The final project will provide methods for deciding which respondents to chase in the context of unit nonresponse and which unit should undergo editing in a context of selecting editing. 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.