Bayesian Shrinkage estimators of the
multivariate normal distribution

Mutwiri Robert Mathenge

doi:https://doi.org/10.14445/22315373/IJMTT-V65I6P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P502

Bayesian Shrinkage estimators of the multivariate normal distribution

Mutwiri Robert Mathenge

Abstract

This paper compares two shrinkage estimators of rates based on Bayesian methods. We estimate the mean θ of the multivariate normal distribution in 𝕽𝒑 , when 𝝈 𝟐 is unknown using the chi-square random variable. The Modified Bayes estimator 𝜹𝑩 ∗ and the Empirical Bayes estimator 𝜹𝑬𝑩 ∗ are considered and the limits of their risk ratios of the maximum likelihood estimator when n and p tend to infinity are obtained.

Keywords

Bayes estimator, Empirical Bayes estimator, James-Stein estimator , Multivariate Gaussian random variable, Modified Bayes estimator, Shrinkage estimator.

References

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Citation :

Mutwiri Robert Mathenge, "Bayesian Shrinkage estimators of the multivariate normal distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 6-14, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P502