Mathematical Sciences: Statistical Problems with Nuisance Parameters

该项目的目标是研究当干扰参数的数目随着观测次数的增加而增加时的渐近估计问题。所得结果可望应用于多维传感器阵列处理。这里的目的是确定最佳可能的渐近性能，并给出一种构造表现这种行为的估计量的方法。类似的问题将在变点估计问题的一个版本中被研究，并且将得到广义贝叶斯估计在Pitman闭性下的可容许性条件。还将研究先验分布与相应贝叶斯估计的频率风险形状之间的关系。这项建议旨在寻找新的方法来获得最优统计程序，并将其应用于信号处理。

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.