Mathematical Sciences: Topics in Nonparametric Analysis andModel Building

建议解决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的问题，还建议开发用于模型诊断的非参数技术，可用于降维并解决特定模型的充分性问题。更准确地说，建议将重点放在与回归系数、相关系数、方差分析分解和主成分等常用线性模型思想对应的过程上。此外，还建议考虑非参数工具用于模型构建、识别和诊断，包括线性、部分线性、可加性等测试。所有要考虑的估计都依赖于曲线和曲面估计所需的平滑参数。研究的很大一部分将解决开发可靠的基于数据的平滑参数选择方法的问题。随着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提高，开发通用模型、概念和程序，用于研究变量之间的关系，以及构建较少依赖于特定假设的模型，变得越来越需要和可能。建议将常用的线性模型思想和技术扩展到这种更一般的环境中，并以更简单的结构评估模型的充分性。

It is proposed to address the question of how intuitive and concise linear model concepts and techniques can be extended to nonparametric settings and it is also proposed to develop nonparametric techniques for model diagnostics that can be used for dimensionality reduction and to address the question of adequacy of particular models. More precisely, it is proposed to focus on procedures that are counterparts to such commonly used linear model ideas as regression coefficients, correlation coefficients, ANOVA decompositions, and principal components. In addition, it is proposed to consider nonparametric tools for model building, identification, and diagnostics including tests for linearity, partial linearity, additivity, etc. All estimators to be considered depend on smoothing parameters needed in estimation of curves and surfaces. A large part of the research will address the problem of developing reliable data-based methods for smoothing parameter selection. With the advent of computer data bases of unprecedented size and complexity and with dramatic increase in computer power, it has become increasingly more desirable and possible to develop general models, concepts, and procedures that can be used to study relationships between variables and to construct models less dependent on specific assumptions. It is proposed to extend commonly used linear model ideas and techniques to this more general setting and to assess the adequacy of models with simpler structure.