Mathematical Sciences: Advanced Methods in Semiparametric and Nonlinear Model Building

该研究项目旨在为参数和半参数环境下的线性和非线性模型构建提供理论和先进的计算方法，包括大数据集和小数据集。部分样条和交互样条以及结合非高斯数据、非线性观测函数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建立。部分重点将放在序列半参数模型构建技术上，该技术适用于具有多个伴随变量的非常大的数据集。还将考虑多元密度估计中的某些模型拟合问题，此外，我们还将介绍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研究中的应用。本研究是在半参数统计方法的一般领域。这些方法所包含的假设比纯参数方法所包含的假设少，但保留了其结构的关键方面。期望得到对统计科学界和一般科学与工程界都有意义的结果。

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.