Estimating Ordered Means of a Bivariate Normal Distribution. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Patra, Lakshmi Kanta; Kumar, Somesh
• Is Part Of: American journal of mathematical and management sciences. Volume 36:Issue 2(2017)
• Page Start: 118
• Page End: 136
• Publication Date: 2017-04-03
• Subjects: Restricted maximum likelihood estimator -- mixed estimator -- minimax estimator -- Generalized Bayes estimator -- Pitman estimator; Operations research -- Periodicals; Management science -- Periodicals; Periodicals; 658.4034
• DOI: 10.1080/01966324.2017.1296797
• Languages: English
• ISSNs: 0196-6324

Abstract

SYNOPTIC ABSTRACT: The problem of estimating ordered parameters arises widely in biological, agricultural, economic, and reliability experiments. Consider a bivariate normal population with unknown mean (θ1, θ2 ), known variances, and known correlation coefficient ρ, where θ1 ⩽ θ2 . The problem of estimation of (θ1, θ2 ) is studied when the loss function used is sum of squared errors. We have considered two cases: equal variances and unequal variances. In both cases, a class of minimax estimators is proposed. These estimators improve upon the usual estimators. A class of admissible estimators is obtained within this class. The minimaxity and admissibility of a generalized Bayes estimator is established. Finally, the risk performance of all the proposed estimators has been compared numerically.