Mathematical Sciences: Statistical Problems with Nuisance Parameters

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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.