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March 2023 Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study
Naresh Garg, Neeraj Misra
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Braz. J. Probab. Stat. 37(1): 101-123 (March 2023). DOI: 10.1214/23-BJPS562


The problem of estimating location (scale) parameters θ1 and θ2 of two distributions when the ordering between them is known apriori (say, θ1θ2) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that θ1θ2. Several of these studies consider specific distributions such that the associated random variables are statistically independent. In this paper, we consider a general bivariate model and a general loss function, and unify various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran’s bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran’s bivariate gamma models.

Funding Statement

This work was supported by the [Council of Scientific and Industrial Research (CSIR)] under Grant [number 09/092(0986)/2018].


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Naresh Garg. Neeraj Misra. "Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study." Braz. J. Probab. Stat. 37 (1) 101 - 123, March 2023.


Received: 1 June 2022; Accepted: 1 January 2023; Published: March 2023
First available in Project Euclid: 27 April 2023

MathSciNet: MR4580886
zbMATH: 07692851
Digital Object Identifier: 10.1214/23-BJPS562

Keywords: Best location equivariant estimator (BLEE) , Best scale equivariant estimator (BSEE) , Brewster–Zidek type estimator , generalized Bayes estimators , Stein type estimator

Rights: This research was funded, in whole or in part, by [EPSRC, EP/L015684/1]. A CC BY 4.0 license is applied to this article arising from this submission, in accordance with the grant's open access conditions

Vol.37 • No. 1 • March 2023
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