Estimation of two ordered normal means when a covariance matrix is known

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restriction...

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Published inStatistics (Berlin, DDR) Vol. 51; no. 5; pp. 1095 - 1104
Main Authors Chang, Yuan-Tsung, Fukuda, Kazufumi, Shinozaki, Nobuo
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.09.2017
Taylor & Francis Ltd
Subjects
Confidence intervals
Covariance matrix
Economic models
Estimating techniques
Linear functions
Maximum likelihood estimators
mean squared error
MLE
Ordered normal means
Pitman nearness criterion
stochastical domination
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ISSN0233-1888
1029-4910
DOI10.1080/02331888.2017.1293059

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Summary:Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67-93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703-715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error.
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ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2017.1293059