scholarly journals Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Andreas Anastasiou ◽  
Robert E. Gaunt
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Error Bounds ◽  
Normal Approximation ◽  
Wasserstein Distance ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Distance Error ◽  
Multivariate Normal Approximation

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

scholarly journals Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

2020 ◽  
Vol 8 (2) ◽  
pp. 507-520
Author(s):  
Abdenour Hamdaoui ◽  
Abdelkader Benkhaled ◽  
Nadia Mezouar
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Unknown Variance ◽  
Multivariate Normal Mean ◽  
Normal Mean

In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested instudying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

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