Mathematical Sciences: Statistical Problems with Nuisance Parameters

数学科学：带有有害参数的统计问题

• 批准号: 9124009
• 负责人: Andrew Rukhin
• 金额: $ 4.02万
• 依托单位: University of Maryland Baltimore County
• 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: 1992-06-15 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9124009&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Problems; Nuisance

The project's goal is to investigate the asymptotic estimation problem when the number of nuisance parameters increases with the number of observations. The application of the obtained results to multidimensional sensor array processing is expected. The aim here is to determine the best possible asymptotic performance and to give a method for constructing an estimator exhibiting this behavior. Similar questions will be studied in a version of the change-point estimation problem and admissibility conditions under Pitman closeness for generalized Bayes estimators will be derived. The relationship between prior distribution and the shape of the frequentist risk of the corresponding Bayes estimator will be also investigated. This proposal is directed towards finding new methods of obtaining optimal statistical procedures with the application to signal processing.

该项目的目标是研究当干扰参数的数量随着观测数量的增加而增加时的渐近估计问题。期望将获得的结果应用于多维传感器阵列处理。这里的目的是确定最佳的渐近性能，并给出一种构建表现出这种行为的估计器的方法。 类似的问题将在变点估计问题的一个版本中进行研究，并且将导出广义贝叶斯估计量在 Pitman 接近度下的容许条件。还将研究先验分布与相应贝叶斯估计量的频率风险形状之间的关系。 该提案旨在寻找新的方法来获得应用于信号处理的最佳统计过程。