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2021•Pakistan Journal of Statistics and Operation ResearchOpen access

On shrinkage estimators improving the James-Stein estimator under balanced loss function

Abdenour Hamdaoui, Mekki Terbeche, Abdelkader Benkhaled

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Mathematics, Estimator, James–Stein estimator, Minimax estimator, Shrinkage estimator, Minimax, Shrinkage, Invariant estimator

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