Minimax estimation of the common variance and precision of two normal populations with ordered restricted means

Lakshmi Kanta Patra (), Suchandan Kayal and Somesh Kumar
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Lakshmi Kanta Patra: Indian Institute of Petroleum and Energy
Suchandan Kayal: National Institute of Technology Rourkela
Somesh Kumar: Indian Institute of Technology Kharagpur

Statistical Papers, 2021, vol. 62, issue 1, No 11, 209-233

Abstract: Abstract Consider two independent normal populations with a common variance and ordered means. For this model, we study the problem of estimating a common variance and a common precision with respect to a general class of scale invariant loss functions. A general minimaxity result is established for estimating the common variance. It is shown that the best affine equivariant estimator and the restricted maximum likelihood estimator are inadmissible. In this direction, we derive a Stein-type improved estimator. We further derive a smooth estimator which improves upon the best affine equivariant estimator. In particular, various scale invariant loss functions are considered and several improved estimators are presented. Furthermore, a simulation study is performed to find the performance of the improved estimators developed in this paper. Similar results are obtained for the problem of estimating a common precision for the stated model under a general class of scale invariant loss functions.

Keywords: Restricted maximum likelihood estimator; Scale invariant loss function; Minimaxity; Stein-type estimator; Brewster and Zidek-type estimator; 62F10; 62C20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01090-2

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