Mathematical Sciences: Some Problems in Nonparametric Function Estimation

数学科学：非参数函数估计中的一些问题

• 批准号: 9024879
• 负责人: Randall Eubank
• 金额: $ 5.94万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024879&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Nonparametric

Nonparametric function estimation is the representation of "noisy" data by a satisfactory smooth function without having to make restrictive assumptions about the function beforehand. The solution lies between artistically connecting all the data points and inadvertently smoothing out salient features of the data. This research will investigate possible definitions of the appropriate balance point between these extremes. Since many functions which differ only slightly may all appear to be satisfactory, definitions of boundaries for "satisfactory function" will also be sought. In addition, corrective techniques will be devised for technical problems with estimation using data near the boundaries of the observable (observed) values.

非参数函数估计是用一个令人满意的光滑函数来表示“有噪声的”数据，而不必事先对该函数做限制性的假设。解决方案在于巧妙地连接所有数据点和无意中平滑数据的显著特征。这项研究将调查这些极端之间适当平衡点的可能定义。由于许多仅略有不同的函数可能看起来都是令人满意的，因此也将寻求“令人满意的函数”的边界的定义。此外，还将针对使用可观测(观察值)值边界附近的数据进行估计的技术问题设计纠正技术。