Some Problems in Nonparametric Function Estimation

研究者继续研究方法/理论/算法的发展和平滑样条方差分析模型的软件实现。通过在功能方差分析结构中包含/排除选定的术语，可以在回归、密度估计和风险率估计的设置中提供丰富的建模选项；流行的加法模型是特例。本阶段研究的具体任务包括：(i)不同性质的变量（如地理位置和季节效应的时间）的单独模型配置，（ii）在通用域上的条件密度估计，其诱导回归模型具有各种响应，包括具有离散，连续和可能的其他类型混合的多元响应。（iii）多变量密度估计的快速计算，使非参数图形模型实际可行；（iv）使用截尾寿命数据和脆弱项进行危害估计。还探讨了非平稳时间序列和尖峰序列的频谱分析。作为广泛使用的（广义）线性模型的非参数扩展，正在开发的方法为研究人员在广泛的应用领域提供了强大的建模工具，以便从他们收集的越来越大的数据集中提取精细特征；在生物医学研究、流行病学、自然资源管理等方面都有记录的应用。拟议研究的最终产品是开源软件，具有友好的用户界面，在一个受欢迎的平台上，具有不同的用户基础，这有利于从业者正在开发的工具的日常使用，从而增强了信息处理的基础设施。

The investigator continues the methodological/theoretical/algorithmic developments and the software implementation of smoothing spline ANOVA models. Through the inclusion/exclusion of selected terms in functional ANOVA structures, rich modeling options are made available in the settings of regression, density estimation, and hazard rate estimation; the popular additive models are special cases. Among specific tasks in this phase of the research are (i) the separate model configurations of variables of different natures such as geographic locations and time for seasonal effect, (ii) conditional density estimation on generic domains which induce regression models with all sorts of responses including multivariate ones with mixtures of discrete, continuous, and possibly other types, (iii) Fast computation for multivariate density estimation which makes nonparametric graphical models practically feasible, and (iv) hazard estimation with censored lifetime data and frailty terms. Also explored are the spectral analysis of non-stationary time series and spike trains.As nonparametric extensions of the widely used (generalized) linear models, the methods being developed provide empowering modeling tools for researchers in a broad spectrum of application areas to extract fine features from the ever larger data sets they collect; documented past applications were found in biomedical studies, epidemiology, natural resource management, etc. The end product of the proposed research is open-source software with a friendly user-interface in a popular platform with a diverse user base, which facilitates the routine use of the tools being developed by practitioners and thus enhances the infrastructure for information-processing.