Mathematical Sciences: Topics in Nonparametric Analysis andModel Building

建议解决的问题是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，它也建议开发非参数技术模型诊断，可用于降维和解决问题的适当性特定的模型。 更确切地说，它建议专注于程序，这些程序是对应于常用的线性模型的想法，如回归系数，相关系数，方差分析分解和主成分。 此外，它建议考虑非参数工具的模型建立，识别和诊断，包括测试的线性，部分线性，可加性等所有估计被认为取决于平滑参数估计所需的曲线和曲面。 大部分的研究将解决的问题，发展可靠的数据为基础的方法，平滑参数的选择。 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增加，开发可用于研究变量之间的关系并构建较少依赖于特定假设的模型的通用模型、概念和程序变得越来越合乎需要和可能。建议将常用的线性模型思想和技术扩展到更一般的环境，并评估结构更简单的模型的充分性。

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.