Topics in Nonparametric Analysis and Model Building

9971301本项目是我们对如何将直观和简洁的线性模型概念和技术扩展到非参数设置以及开发用于模型诊断、降维和评估特定类别模型的充分性的非参数技术的研究的继续。本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，其中条件作用于限制在邻域的协变量。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函数估计。要考虑的许多估计量依赖于曲线和曲面估计所需的平滑参数。研究的很大一部分解决了开发可靠的基于数据的平滑参数选择方法的问题。用渐近方法和蒙特卡罗模拟研究了估计量的性质。空前规模和复杂性的计算机数据库的出现，以及计算机能力的急剧增长，使得开发更灵活的模型、概念和过程成为可能。这些可以用来研究变量之间的关系，并在不需要依赖严格的全局假设的情况下构建模型。最近在统计方面的许多工作都解决了对更一般和更灵活的方法的需求。本研究进一步扩展了这项工作，特别关注与许多常用线性模型概念对应的程序，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.