Some Problems in Nonparametric Function Estimation

非参数函数估计中的一些问题

• 批准号: 0705961
• 负责人: Chong Gu
• 金额: $ 18.01万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0705961&HistoricalAwards=false
• 关键词: Some; Problems; Nonparametric; Function; Estimation

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.

研究者继续进行方法/理论/算法开发和平滑样条方差分析模型的软件实现。 通过在函数ANOVA结构中包含/排除选定的项，在回归、密度估计和风险率估计的设置中提供了丰富的建模选项;流行的加性模型是特例。 在这个研究阶段的具体任务是（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）通用域上的条件密度估计，其诱导具有各种响应的回归模型，包括具有离散，连续和可能其他类型混合的多变量模型，（三）快速计算的多元密度估计，使非参数图形模型实际可行，和（四）风险估计与删失寿命数据和脆弱性条款。 本文还探讨了非平稳时间序列和尖峰脉冲序列的谱分析。（广义）线性模型，正在开发的方法为广泛应用领域的研究人员提供了授权建模工具，以从他们收集的越来越大的数据集中提取精细特征;有文献记载的过去的应用被发现在生物医学研究，流行病学，自然资源管理，所提出的研究的最终产品是具有友好用户界面的开源软件，该软件在具有不同用户群的流行平台上，这有助于从业人员开发的工具的日常使用，从而增强了信息处理的基础设施。