Bayesian Wavelet Stein’s Unbiased Risk Estimation of Multivariate Normal Distribution Under Reflected Normal Loss

Hamid Karamikabir (), Nasrin Karamikabir (), Mohammad Ali Khajeian () and Mahmoud Afshari ()
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Hamid Karamikabir: Persian Gulf University
Nasrin Karamikabir: Hamedan Branch, Islamic Azad University
Mohammad Ali Khajeian: Persian Gulf University
Mahmoud Afshari: Persian Gulf University

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-20

Abstract: Abstract In this paper, we consider the generalized Bayes estimator of mean vector parameter for multivariate normal distribution with unknown mean vector and covariance matrix under reflected normal loss function. We also prove admissibility and minimaxity of the generalized Bayes estimator. We obtain Stein’s unbiased risk estimator (SURE) threshold based on generalized Bayes SURE estimator and we find the wavelet shrinkage generalized Bayes SURE estimator. At the end, we check the performance of this estimator and we provide two real examples.

Keywords: Generalized Bayes; Multivariate normal distribution; Reflected normal loss; Threshold; Wavelet shrinkage; 62F10; 62J07; 65T60 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09992-3

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