Nonparametric Inference and Prediction for Complex Data by Data Depth, Confidence Distribution and Monte Carlo Method

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In the era of information and data explosion, the demand of effective data analysis methods for solving problems and assisting decision-making has never been greater. This demand comes from all domains, from modern scientific endeavors, government and industry policy-making, financial and business strategic planning, to even the most basic social-economic studies. Despite recent great strides made in mathematical and statistical sciences, many new challenges have been brought to the fore by the need of confronting the pervasive massive, diverse and complex data. The PIs of this project will develop several novel approaches to addresses general inference and prediction problems in settings where data sources are diverse or where the conventional statistical large sample theory fails to apply.Motivated by several real applications, this project will develop nonparametric approaches for: individualized inference from diverse data sources (referring to as i-Fusion), prediction for complex data, and exact inference for estimating equations. Underlying these proposed approaches is the common tool kit consisting of data depth, confidence distribution and Monte Carlo methods. The proposed approaches are expected to be broadly applicable, efficient and computationally feasible. Three specific projects are: A. Develop the new i-Fusion for drawing efficient individualized inference by effectively combining learnings from relevant data sources; B. Develop CD Monte-Carlo methods for the exact inference for estimating equations; C. Develop nonparametric predictive distributions for efficient prediction with complex data. The proposed methodologies will be developed with theoretical support and applied to the areas: i) prediction of volumes of application submissions to interrelated units in a government agency; and ii) performance forecast for individual companies by borrowing information possibly shared by others, and, potentially, iii) identification of hot spots in tracking glacial striation around the globe. These applications are motivated by the PIs' ongoing collaborative projects with the CCICADA of Department of Homeland Security, and possibly Rutgers Climate Risk and Resilience Initiative. These projects involve real databases and are ideally suited for engaging and training students and new researchers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.