Multidimensional Mixture Regression Models: Estimation and Inference

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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.