Multidimensional Mixture Regression Models: Estimation and Inference

本提案的总体目标是为研究由回归函数描述的回归模型提供一个统一的框架，该回归函数是多维单峰函数的加权和。假设多维回归组件形状相似，但通过一组参数可识别。提出的研究重点是推进方法，以解决提出的多维混合回归模型的估计和推理中的基本统计问题。提出的统计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，但也有助于其他应用，如使用乳腺计算机断层扫描（CT）识别和分类病变或肿瘤块，以及识别和估计天空图像中的天文物体。该研究的目的是利用核磁共振技术预测稳定的蛋白质结构和确定复杂分子，同时利用乳腺CT技术更准确地检测病变或肿瘤肿块。

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.