Optimal Shrinkage Estimation for Heteroscedastic Data

异方差数据的最优收缩估计

• 批准号: 1510446
• 负责人: Samuel Kou
• 金额: $ 30.41万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1510446&HistoricalAwards=false
• 关键词: Optimal; Shrinkage; Estimation; Heteroscedastic; Data

Shrinkage estimators are powerful statistical methods that have profound impact in scientific and engineering applications. They provide efficient tools to pool information from related populations for simultaneous inference -- the data on each population alone often do not lead to the most effective estimation, but by pooling information from the related populations together one can often obtain more accurate estimates for each individual population. Examples of the applications of shrinkage estimators include the analysis of healthcare systems (quality of hospital services, etc.), the analysis of education programs (the effectiveness of teaching programs), the assessment of medical treatments (pooling information from multiple studies or clinical trials), the ranking of multiple genes on their association with diseases, and the comparison of multiple manufacturing processes. This research project will investigate shrinkage estimations in the context of heterogeneous data, aiming to identify optimal ways to conduct shrinkage estimation in various settings.This research project studies and identifies risk-optimal shrinkage estimators under parametric as well as semi-parametric settings for heteroscedastic data. In addition to thorough theoretical investigation, the project includes comprehensive numerical studies and real applications. The research topics include the investigation of optimal shrinkage estimators for heteroscedastic data from non-Gaussian exponential families; the investigation of optimal shrinkage estimators for heteroscedastic data from location-scale families; and the investigation of optimal shrinkage estimators for heteroscedastic data from linear regression models. The research aims to advance the theoretical understanding of shrinkage estimators and also provide powerful techniques for the analysis of data in medical, natural and social sciences, and engineering.

收缩估计量是一种在科学和工程应用中具有深远影响的强有力的统计方法。它们提供了有效的工具，可以从相关人群中汇集信息，进行同步推断----单独使用每个人群的数据往往不能得出最有效的估计，但通过将相关人群的信息汇集在一起，往往可以获得每个人群的更准确估计。收缩估计器的应用实例包括医疗保健系统的分析（医院服务质量等），教育计划的分析（教学计划的有效性），医学治疗的评估（汇集来自多项研究或临床试验的信息），多个基因与疾病相关性的排名，以及多个制造过程的比较。本研究将探讨异质数据背景下的收缩估计，旨在确定在各种设置下进行收缩估计的最佳方法。本研究项目研究并确定异方差数据在参数和半参数设置下的风险最优收缩估计。除了深入的理论研究外，该项目还包括全面的数值研究和真实的应用。研究主题包括非高斯指数族异方差数据的最优收缩估计的研究;位置尺度族异方差数据的最优收缩估计的研究;以及线性回归模型异方差数据的最优收缩估计的研究。该研究旨在推进对收缩估计的理论理解，并为医学，自然和社会科学以及工程中的数据分析提供强大的技术。