Mathematical Sciences: Advanced Methods in Semiparametric and Nonlinear Model Building

本课题的研究目的是为我国的农业生产提供理论和先进的 线性和非线性模型建立的计算方法 参数化和半参数化环境， 小数据集。 局部样条和交互样条， 结合非高斯数据、非线性 观察泛函和先验不等式约束将 适用于大规模多变量半参数模型 建设 部分重点将放在顺序上 半参数建模技术适用于非常大的 有几个伴随变量的数据集。 一定的借鉴 多元密度估计中的拟合问题也将被 考虑，因为将方法近似和显示 非线性统计模型的似然轮廓和 这些技术的应用调查 几类非线性模型中的多参数相互作用 制剂。 本研究是在一般领域的半参数 统计方法 这种方法包含较少的假设 比纯参数方法中所体现的要多，但保留了关键的 其结构方面。 两项结果均具有显著性 统计科学界和一般科学界， 工程界期待。

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.