Abstract
In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.
Highlights
The problem of estimation the mean parameters is the most widely used statistical tool applied in almost all fields
This problem has been attracted the attention of many researchers for multivariate normal distribution
We aim to develop shrinkage estimators that are both minimax and capable of effective risk reduction over the usual estimator
Summary
The problem of estimation the mean parameters is the most widely used statistical tool applied in almost all fields. The authors showed that if the shrinkage function ψ (respectively φ) satisfies the new conditions different from the known results in the literature, the estimator δψ (respectively δφ) is minimax. When both sample size and the dimension of parameters space tend to infinity, they studied the behaviour of risks ratio of these estimators to the MLE. Sanjari and Asgharzadeh(2004) have considered the model: X1, ..., Xn to be a random sample from Np θ, σ2Ip with σ2 known and the aim is to estimate the parameter θ They studied the admissibility of the estimator of the form aX + b under the balanced loss function. The proofs of some our main results are collected in the Appendix
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