Simultaneous Estimation Of Mean Vectors In Multidimensional Normal Hierarchical Models

In portfolio analysis and other scientific fields,hierarchical models have been widely studied and used,and gradually become important statistical models.Empirical Bayes estimation is an effective method to study the parameter estimation of hierarchical models.It can be used to reduce the estimation risk and explain the uncertainty of the model in portfolio selection.This thesis focuses on the field of portfolio analysis,and studies the simultaneous estimation problem of mean in multidimensional normal hierarchical models from the perspective of empirical Bayes.Firstly,by employing the Stein's unbiased estimate of risk(SURE),with the mean square loss,two new SURE type shrinkage estimates are constructed for the mean vectors in the multidimensional normal hierarchical models.Secondly,under the mild conditions,we prove the optimal asymptotic properties of the newly proposed estimators.Finally,this thesis gives some examples of numerical simulations,comparing the oracle loss and the existing methods,which illustrate the proposed method.At the same time,this thesis also applies the established estimator to the real data,which further demonstrate the superiority of the proposed method.