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

在这项研究中，开发了包含参数、光滑和不连续成分的统计模型，并将其应用于涉及高维回归、曲线样本作为观测、或变化点和跳跃不连续的问题。这些模型的动机是科学问题，包括对研究对象群体样本的纵向分析、对描述疾病传播的空间发病率数据的分析以及可能发生不连续性的儿童的成长。这还包括包含协变量对响应曲线样本影响的模型，以及在DNA序列分割和图像分析中的边缘检测背景下具有不连续元素的模型的构建。设计了拟合模型的方法，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。分析了这些方法的性质，并将它们应用于与科学问题有关的数据。本研究通过提供创新的统计方法，有助于解决重大科学问题。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老龄化过程，这对21世纪的社会安全和医疗保健有潜在影响。为了从许多队列中提取和组合有关观察到的个体生存的信息，需要复杂的方法。另一个问题是描述和分析艾滋病和其他流行病随时间的空间传播。第三个问题是DNA序列的分割，这可能会使这些片段与生物功能相关联。这些和相关的问题可以放到本研究中开发的新统计模型的框架中。这些模型的应用使我们能够对这些复杂问题的基础科学方面获得重要的新见解。

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.