Estimation of Order Restricted Normal Means when the Variances Are Unknown and Unequal

Authors

  • Najmeh Pedram Department of Statistics, Persian Gulf University, Bushehr, Iran
  • Abouzar Bazyari Department of Statistics, Persian Gulf University, Bushehr, Iran

DOI:

https://doi.org/10.17713/ajs.v46i2.446

Abstract

In the present paper, two normal distributions with parameters ?i and ?i2 where there is an order restriction on the means when the variances are unknown and unequal are considered. Under the squared error loss function, a necessary and sufficient condition for the plug-in estimators to improve upon the unrestricted maximum likelihood estimators uniformly is given. Also under the modified Pitman nearness criterion; a class of estimators is considered that reduce to the estimators of a common mean when the unbiased estimators violate the order restriction. It is shown that the most critical case for uniform improvement with regard to the unbiased estimators is the one when two means are equal. To illustrate the results, two numerical examples are presented.

References

Professor Fortunato Pesarin

Email: [email protected]

Department of Statistical Sciences, Padova University, Padova, Italy

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Additional Files

Published

2017-01-04

How to Cite

Pedram, N., & Bazyari, A. (2017). Estimation of Order Restricted Normal Means when the Variances Are Unknown and Unequal. Austrian Journal of Statistics, 46(2), 3–17. https://doi.org/10.17713/ajs.v46i2.446

Issue

Section

Articles