Semiparametric and Nonparametric Inferences

半参数和非参数推论大多数涉及数据的科学问题和许多医学研究问题可以看作是对反应变量和许多潜在解释变量之间的关联的调查。回归分析、小波技术、分层贝叶斯分析和神经网络都包括在可以用来解决这些问题的工具中。计算机技术的最新进展使收集大型数据集变得更容易，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。这项研究涉及从信号处理到生存数据分析的几个相关统计问题。这项研究包括在两个领域进一步开发用于模型拟合和推理的方法和计算工具。在第一个领域，研究开发了随机筛选法和确定性筛选法的新技术，每一种技术都以新的方式扩展了现有的技术。在第二个领域中，研究了半参数和非参数贝叶斯与极大似然推理之间联系的基本问题，并构造了函数推理的置信度区间和置信度。应用领域包括生存分析和信号处理。从这次调查中获得的知识预计将给许多其他统计领域带来巨大好处，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.