Mathematical Sciences: Statistical Problems with Nuisance Parameters

该项目的目标是研究渐近 估计问题时的滋扰参数的数量 随着观察次数的增加而增加。的应用 得到的结果进行多维传感器阵列处理， 预期这里的目的是确定最好的可能 渐近性能，并给出了一种方法， 表现出这种行为的估计器。 类似的问题将在 研究了变点估计问题的一个版本， 皮特曼封闭下广义可容许条件 贝叶斯估计将被导出。先验之间的关系 的频率论风险的分布和形状， 相应的贝叶斯估计也将进行研究。 该建议旨在寻找新的方法， 获得最佳的统计程序与应用， 信号处理

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.