Topics in Nonparametric Analysis and Model Building

9971301这个项目是我们的研究如何直观和简洁的线性模型的概念和技术可以扩展到非参数设置和非参数技术的发展模型诊断，降维，并评估特定类别的模型的充分性的问题的继续。 在这项研究中考虑的一些程序是基于熟悉的回归，协方差和相关系数的条件版本，其中的条件是对协变量限制在附近。 邻域的大小作为分辨率尺度，在多个尺度上测量和总结响应对协变量的依赖性。 其他程序是曲线或曲面估计和分布的积分泛函估计。 要考虑的许多估计依赖于估计曲线和曲面所需的光滑参数。 很大一部分的研究解决的问题，制定可靠的数据为基础的方法，平滑参数的选择。使用渐近方法和Monte Carlo simulation.The计算机数据库的出现前所未有的规模和复杂性，以及计算机能力的急剧增加，使得更灵活的模型，概念和程序的发展是可取的和可能的。 这些可以用来研究变量之间的关系，并建立模型，而不需要依赖于严格的全球假设。 最近在统计方面的许多工作都涉及到对更普遍和灵活的方法的需要。 这项研究进一步扩展了这项工作，特别关注与许多常用的线性模型概念相对应的程序，并使用直观和熟悉的想法揭示数据中的重要特征。所开发的程序适用于金融、经济、保险、医疗和其他数据。

9971301 This project is the continuation of our research on the question of how intuitive and concise linear model concepts and techniques can be extended to nonparametric settings and on the development of nonparametric techniques for model diagnostics, dimensionality reduction, and assessing adequacy of particular classes of models. Some of the procedures considered in this research are based on conditional versions of the familiar regression, covariance, and correlation coefficients, where the conditioning is on covariates restricted to neighborhoods. The size of the neighborhood serves as a resolution scale, and dependence of the response on the covariates is measured and summarized at multiple scales. Other procedures are curve or surface estimators and estimators of integral functionals of distributions. Many of the estimators to be considered depend on smoothing parameters needed in estimation of curves and surfaces. A large part of the research addresses the problem of developing reliable data-based methods for smoothing parameter selection. Properties of estimators are studied using both asymptotic methods and Monte Carlo simulations.The advent of computer data bases of unprecedented size and complexity, and the dramatic increase in computer power, makes desirable and possible the development of more flexible models, concepts, and procedures. These can be used to study relationships between variables and to construct models without the need of relying on rigid global assumptions. Much of the recent work in statistics has addressed this need for more general and flexible methods. This research further extends this work with a special focus on procedures that are counterparts to many commonly used linear model concepts and that expose important features in the data using intuitive and familiar ideas. The developed procedures are applied to financial, economic, insurance, medical, and other data.