Mathematical Sciences: Inference for Nonparametric Function Estimators

数学科学：非参数函数估计量的推理

• 批准号: 9300918
• 负责人: Randall Eubank
• 金额: $ 6万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300918&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inference; Nonparametric; Function

A number of inference problems in nonparametric function estimation will be investigated during the course of this project. The problems to be considered include i) estimation of breakpoints for regression functions or their derivatives, ii) development of practical confidence bands for use in nonparametric regression, iii) construction of diagnostic goodness-of-fit tests using nonparametric function estimation methodology in a variety of settings, including censored data and additive models, and iv) spline smoothing with correlated errors. It is often reasonable to believe in many areas of science, such as biology, engineering, psychology, etc., that the data being collected is produced by two components: a nonrandom component, representing a characteristic of nature common to all individuals or subjects, and a random component that accounts for individual variation. This nonrandom component represents the understandable or predictable aspect of the phenomenon being studied and is therefore of considerable interest. Nonparametric function estimation is an area of statistics concerned with the development of flexible methods for estimating or describing the nonrandom components of data. The current research project deals with a variety of problems in nonparametric function estimation including i) the development of procedures for estimating a point where an abrupt change has occurred in some phenomenon (e.g., locating a point of sudden change in the discharge of water from a river or prices of a commodity) ii) the construction of accuracy measures (similar to those associated with popularity polls, etc.) to accompany nonparametric function estimators and iii) the development of statistical methods to assess the accuracy of models that have been postulated by scientists to describe various processes they are studying.

在该项目过程中将研究非参数函数估计中的许多推理问题。要考虑的问题包括 i) 估计回归函数或其导数的断点，ii) 开发用于非参数回归的实用置信带，iii) 在各种设置（包括审查数据和加性模型）中使用非参数函数估计方法构建诊断拟合优度检验，以及 iv) 具有相关误差的样条平滑。 在许多科学领域，例如生物学、工程学、心理学等，通常合理地相信，所收集的数据是由两个部分产生的：非随机部分，代表所有个人或受试者共有的自然特征，以及解释个体差异的随机部分。这种非随机成分代表了所研究现象的可理解或可预测的方面，因此引起了相当大的兴趣。非参数函数估计是统计学的一个领域，涉及开发用于估计或描述数据非随机分量的灵活方法。 当前的研究项目涉及非参数函数估计中的各种问题，包括i）开发用于估计某些现象中发生突变的点的程序（例如，定位河流排水量或商品价格的突然变化点）ii）与非参数函数估计器一起建立精度测量（类似于与民意调查等相关的测量）以及iii）统计方法的开发 评估科学家为描述他们正在研究的各种过程而假设的模型的准确性。