Multidimensional Mixture Regression Models: Estimation and Inference

该提案的总体目标是提供一个统一的框架，用于研究由多维单峰函数加权和的回归函数描述的回归模型。多维回归分量被假设为形状相似，但可通过一组参数识别。该研究的重点是推进多维混合回归模型的估计和推断中的基本统计问题的方法，该方法将有助于生物分子核磁共振（NMR）研究领域，这将有助于发现生物分子结构所需的定量论证，而且还涉及其它应用，例如使用乳房计算机断层摄影（CT）对病变或肿瘤块的识别和分类，以及对天空图像中的天文物体的识别和估计。拟议研究的终点是稳定的蛋白质结构预测和复杂分子的测定，使用NMR技术沿着使用乳腺CT技术更准确地检测病变或肿瘤块。

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.