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论/理论/算法开发以及平滑样条ANOVA模型的软件实现。 通过在功能方差分析结构中包含/排除选定的项，可以在回归，密度估计和危害率估计的设置中提供丰富的建模选项；流行的添加剂模型是特殊情况。 在研究的这一阶段中，特定任务之间是（i）不同出性的变量的单独模型配置，例如地理位置和季节性效应的时间，（ii）对通用域的有条件密度估计，这些密度估算具有各种响应的回归模型，这些响应模型具有各种响应，包括多变量，包括具有依赖性，持续性和其他类型（III）快速计算的多变量，以便进行多变量模型，以实现多种响应，以实现多种响应。实际上是可行的，并且（iv）危害估计具有审查的终身数据和脆弱的术语。 还探讨了非平稳时间序列和尖峰列表的光谱分析。作为广泛使用（广义）线性模型的非参数扩展，开发的方法为研究人员提供了赋权建模工具，以在广泛的应用领域中从其收集到的较大数据集中提取出色的特征。在生物医学研究，流行病学，自然资源管理等中发现了过去的应用。拟议的研究的最终产品是开源软件，在一个流行的平台中具有友好的用户界面，具有多样化的用户基础，从而有助于实践者开发的工具，从而增强了基础结构的信息处理。