Mathematical Sciences: Mathematical Statistics on Singular Problems

数学科学：奇异问题的数理统计

• 批准号: 9207072
• 负责人: Richard Liu
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207072&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistics; Singular; Problems

Singular functional estimation problems cover an extremely large portion of statistical theory. Some procedures with optimal rates have been well established; but recent work on white noise problems has led to a unified approach based on the modulus of the functional. This approach gives optimal or near optimal procedures quite simply for many important statistical problems. For some statistical estimation problems, optimal methods are well known, but for many more either optimality of the methodology is uncertain or its efficiency is unknown. This research will produce generally efficient procedures which can have many scientific applications, for example complex problems like reconstruction of the "true image" from tomography or other imaging techniques. This unified approach to estimation should find applications in engineering, biology, economics and other fields where practical and theoretical scientific problems are framed in terms of statistical models.

单数功能估计问题涵盖了统计理论的极大部分。 一些具有最佳速率的程序已经确定；但是，最近关于白噪声问题的工作导致了基于功能模量的统一方法。 对于许多重要的统计问题，这种方法给出了最佳或接近最佳的程序。 对于某些统计估计问题，最佳方法是众所周知的，但是对于更多的方法，方法是不确定的，或者其效率尚不清楚。 这项研究将产生一般有效的程序，这些程序可以具有许多科学应用，例如复杂的问题，例如从层析成像或其他成像技术中重建“真实图像”。这种统一的估算方法应在工程，生物学，经济学和其他领域中找到应用，在这些领域中，实际和理论科学问题是根据统计模型构成的。