A unified study for estimation of order restricted parameters of a general bivariate model under the generalized Pitman nearness criterion

Naresh Garg () and Neeraj Misra ()
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Naresh Garg: Indian Institute of Technology Kanpur
Neeraj Misra: Indian Institute of Technology Kanpur

Statistical Papers, 2024, vol. 65, issue 4, No 3, 1947-1983

Abstract: Abstract We consider component-wise estimation of order-restricted location/scale parameters of a general bivariate location/scale probability distribution under the Generalized Pitman Nearness (GPN) criterion, with a general loss function. In contrast to earlier studies on the same theme, that were mainly focused to specific probability distributions having independent components (marginals), we consider a general bivariate location/scale model and unify various studies made in the literature by developing some general results. These results are useful in finding improvements over arbitrary location/scale equivariant estimators, satisfying certain conditions, under the GPN criterion. In particular, under certain conditions, our results provide improvements over unrestricted Pitman nearest location/scale equivariant estimators and restricted maximum likelihood estimators. We illustrate the usefulness of these results through their applications to specific probability models. Additionally, we conduct a simulation study to compare the performances of different estimators under the GPN criterion with a specific loss function. Furthermore, we provide a real-life data analysis to demonstrate implementation of proposed estimators.

Keywords: Generalised Pitman nearness criterion; Pitman nearness estimator location equivariant estimator; Pitman nearness criterion; Restricted parameter space; Scale equivariant estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01464-7

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