Mathematical Sciences: Advanced Methods in Semiparametric and Nonlinear Model Building

数学科学：半参数和非线性模型构建的高级方法

• 批准号: 8701836
• 负责人: Grace Wahba
• 金额: --
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1988-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701836&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Advanced; Methods; Semiparametric

This research project is to provide theoretical and advanced computational methods for linear and nonlinear model building in both a parametric and a semiparametric context, with both large and small data sets. Partial and interaction splines and combining the problems of non-Gaussian data, nonlinear observation functionals and apriori inequality constraints will be used in large scale multivariate semi-parametric model building. Part of the emphasis will be on sequential semiparametric model building techniques suitable for very large data sets with several concomitant variables. Certain model fitting problems in multivariate density estimation will also be considered, as will methods for approximating and displaying likelihood contours for nonlinear statistical models and the application of these techniques to the investigation of multiparameter interactions in several types of non-linear model formulations. This research is in the general area of semi-parametric statistical methods. Such methods incorporate fewer assumptions than embodied in pure parametric methods but retain critical aspects of their structure. Results with significance for both the statistical sciences community and the general science and engineering community are expected.

该研究项目旨在为参数化和半参数化背景下的线性和非线性模型构建提供理论和先进的计算方法，无论是大型还是小型数据集。 部分样条和交互样条以及结合非高斯数据、非线性观测泛函和先验不等式约束的问题将用于大规模多元半参数模型的构建。 部分重点将放在适用于具有多个伴随变量的非常大的数据集的顺序半参数模型构建技术上。 还将考虑多元密度估计中的某些模型拟合问题，以及用于近似和显示非线性统计模型的似然轮廓的方法以及这些技术在几种类型的非线性模型公式中的多参数相互作用的研究中的应用。 这项研究属于半参数统计方法的一般领域。 与纯参数方法相比，此类方法包含的假设更少，但保留了其结构的关键方面。 预计结果对统计科学界和一般科学与工程界都具有重要意义。