Curve Estimation Models for High-dimensional, Multivariate, and Discontinuous Data

穆勒 在这项研究中，统计模型，其中包含参数，光滑和不连续的组件开发和应用的问题，涉及高维回归，样本的曲线作为观察，或变点和跳跃不连续。这些模型的动机是科学问题，包括纵向分析的样本队列的科目，分析的空间发病率数据描述疾病的传播，和儿童的成长，其中可能会出现不连续性。这也包括模型，其中包括响应曲线的样本上的协变量的影响，并在DNA序列的分割和图像分析中的边缘检测的背景下与不连续元素的模型的构建。设计用于拟合模型的方法，其通常涉及使用平滑技术、广义线性模型和估计方程作为构建块的复杂迭代算法。这些方法的属性进行了分析，并将其应用于有关的科学问题的数据。 这项研究通过提供创新的统计方法，为解决重大科学问题做出了贡献。其中一个问题是人口中老年人的死亡率，以及基于动物模型的衰老过程，对21世纪的社会保障和医疗保健有潜在影响。需要采用复杂的方法，以便从许多群组中提取和联合收割机综合关于观察到的个人生存情况的信息。另一个问题是描述和分析艾滋病和其他流行病随着时间推移的空间传播。第三个问题是DNA序列的分割，这可能会使片段与生物功能相关联。这些问题和相关问题可以纳入本研究中开发的新统计模型的框架中。这些模型的应用允许获得重要的新见解，这些复杂问题的基本科学方面。

Mueller In this research, statistical models which contain parametric, smooth and discontinuous components are developed and applied to problems which involve high-dimensional regression, samples of curves as observations, or change-points and jump discontinuities. These models are motivated by scientific problems including the longitudinal analysis of samples of cohorts of subjects, the analysis of spatial incidence data describing the spread of diseases, and the growth of children, where discontinuities may occur. This also includes models which incorporate the influence of covariates on a sample of response curves, and the construction of models with discontinuous elements in the context of segmentation of DNA sequences and of edge detection in image analysis. Methods for fitting the models are devised, which typically involve complex iterative algorithms using smoothing techniques, generalized linear models and estimating equations as building blocks. The properties of these methods are analyzed and they are applied to data pertaining to the scientific problems. This research contributes to the solution of major scientific problems by providing innovative statistical methods. One such problem is the mortality of the older segments of a population and what one can say about the aging process based on animal models, with potential impact on social security and health care in the 21st century. Sophisticated methods are needed in order to extract and combine the information on the observed survival of the individuals from many cohorts. Another problem is to describe and analyze the spatial spread of AIDS and of other epidemics as time passes. A third problem is the segmentation of DNA sequences which then may allow for association of the segments with biological functions. These and related problems can be put into the framework of the new statistical models which are developed in this research. The application of these models allows to gain important new insight s into fundamental scientific aspects of these complex problems.