The overarching objective of this proposal is to provide a unified framework for the study of a regression model described by a regression function that is a weighted sum of multi-dimensional unimodal functions. The multidimensional regression components are assumed similar in shape but identifiable through a set of parameters. The focus of the proposed research is to advance methodology that addresses fundamental statistical problems in estimation and inference of the proposed multidimensional mixture regression model.

The proposed statistical methodology will contribute to the field of biomolecular Nuclear Magnetic Resonance (NMR) studies, which will aid in the quantitative argumentation needed in discovery of biomelecule structures, but also to other applications such as identification and classification of lesions or tumor masses using breast computed tomography (CT) and identification and estimation of astronomical objects in images of the sky. The endpoint of the proposed research is stable protein structure predictions and determination of complex molecules using NMR technology along with more accurate detection of lesions or tumor masses using breast CT technology.

Project Report

The proposed research has led to important theoretical findings for models that are commonly applied to biomedical applications, including discovery of protein structures and identification of lesions or tumor masses using breast computed tomography (CT). The underlying results from this research will allow for accurate identification of components in a system that can be modeled using the regression approach in this proposal. The methods developed are based on theoretical results that allow computationally inexpensive implementations. In the first project, the PI and a collaborator derives a statistical test that leads to accurate de-mixing of components; its implementation relies on an approximation that is validated as providing accurate statistical results. In the second project, the Principal Investigator and a doctoral student provided theoretical insights on what components in the system can be discovered given the turbulence in the system and the resolution of the observations. The Principal Investigator has mentored and advised two doctoral students in research relevant to two of the activities in this proposal. The research has been disseminated through publication of two research articles and one presentation delivered by one doctoral student. The proposed research will be available as a statistical software implementation for further investigation and application. The Principal Investigator has collaborated on one research activity with a researcher in an academic institution in Canada, hence disseminating this research internationally.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Gabor J. Szekely
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Georgia Tech Research Corporation
United States
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