Collaborative Research: Nonparametric smoothing for data with multiple components

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Over the decades, nonparametric smoothing has become a standard tool for many classical statistical problems owing partly to the boom of computing power. Relatively little work has addressed nonparametric smoothing in more complex settings where data have multiple components and the analysis requires nontrivial integration of techniques from different statistical domains. This project concerns three types of such complex data that are common in practice, and propose a suite of nonparametric statistical models in the framework of smoothing spline ANOVA models. Existing methods for these three types of data are mainly parametric and semi-parametric, whose practical uses are limited by their strong assumptions on the dependence structure of response on predictors or covariates. The nonparametric methods proposed in this project, combining nonparametric Gaussian regression, nonparametric logistic regression and nonparametric hazard rate estimation, offer much more flexibility and are extremely useful at the exploratory stage when researchers are not certain of the pattern of dependence. Accompanied with the proposed models are useful inference tools such as model selection and confidence intervals. Asymptotic properties of the estimates are investigated through a combination of asymptotic analysis techniques for nonparametric smoothing splines, semiparametric estimation, and measurement error models. Major challenges to today's federal government, such as health care reform, education reform and financial system improvement, provide data with complex structures that call for accurate, informative and flexible data analysis methods. The proposed nonparametric smoothing methods provide an innovative direction for developing analysis tools appropriate for tackling these challenges. These types of data can also be found in a broad spectrum of scientific fields such as biological sciences, economics, social sciences, psychological sciences, and biomedical studies. This research will advance education and training of graduate and undergraduate students in the relevant statistical areas.