Mathematical Sciences: Topics in Nonparametric Analysis and Model Building

数学科学：非参数分析和模型构建主题

• 批准号: 9306245
• 负责人: Alexander Samarov
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306245&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Nonparametric; Analysis

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.

建议解决如何直观和 简洁的线性模型概念和技术可以扩展到 非参数设置，并建议开发 模型诊断的非参数技术， 降维和解决 具体模型的适用性。 更确切地说，建议 重点放在与这些常用的 线性模型的思想作为回归系数，相关性 系数、ANOVA分解和主成分。 在 此外，建议考虑非参数工具， 模型构建、识别和诊断，包括测试 用于线性、部分线性、可加性等。所有估计量 取决于所需的平滑参数， 曲线和曲面的估计。 很大一部分的研究 将解决开发可靠的基于数据的 平滑参数选择的方法。 随着空前规模的计算机数据库的出现 和复杂性，以及计算机能力的急剧增加， 已经变得越来越可取和可能发展 一般模型、概念和程序，可用于 研究变量之间的关系并构建模型 更少地依赖于特定的假设。建议延长 常用的线性模型的思想和技术，这更多 一般设置，并评估模型的适当性， 更简单的结构。