Semiparametric and Nonparametric Inferences

半参数和非参数推理大多数涉及数据的科学问题和许多医学研究问题都可以看作是对响应变量和一些潜在解释变量之间关系的调查。回归分析、小波技术、层次贝叶斯分析和神经网络都包含在解决这类问题的工具集合中。计算机技术的最新进步使收集大型数据集变得更加容易，这反过来又需要更复杂的科学理论。因此，高维半参数和非参数技术成为分析数据的有力工具。本研究涉及几个相关的统计问题，从处理信号到分析生存数据。研究包括两个方面的模型拟合和推理的方法和计算工具的进一步发展。在第一个领域，研究开发了随机筛法和确定性筛法这两种新技术，它们都以新的方式扩展了现有的技术。第二部分研究了半参数贝叶斯与非参数贝叶斯之间的联系以及极大似然推理的基础问题，构建了函数推理的置信带和置信区间。应用领域包括生存分析和信号处理。在这项调查中获得的知识有望给许多其他统计领域带来巨大的好处，并将在各种复杂的科学问题中发挥作用。

Semiparametric and nonparametric inferences Most scientific problems involving data and many medical research problems can be viewed as an investigation into the association between a response variable and a number of potential explanatory variables. Regression analysis, wavelet techniques, hierarchical Bayesian analysis, and neural networks are included in the set of tools that can be brought to bear on such problems. Recent advances in computer technology make it easier to collect large data sets, which in turn demand more complex scientific theories. Hence high-dimensional semiparametric and nonparametric techniques become powerful tools for analyzing data. This research concerns several related statistical problems ranging from processing signals to analyzing survival data. The research includes the further development of methodologies and computational tools for model fitting and inference in two areas. In the first area, the research develops new techniques of random-sieve methodology and deterministic sieve methodology, each of which expands existing techniques in novel ways. In the second area, the research studies foundational issues of the connection between semiparametric and nonparametric Bayesian and maximum likelihood inference, and constructs confidence bands andintervals for function inference. The areas of application include survival analysis and signal processing. The knowledge gained in this investigation is expected to bring great benefit to many other statistical areas and will be useful in a variety of complex scientific problems.