Estimating the shape parameter of a Pareto distribution under restrictions

Yogesh Tripathi (), Somesh Kumar () and Constantinos Petropoulos ()

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 1, 111 pages

Abstract: In this paper estimation of the shape parameter of a Pareto distribution is considered under the a priori assumption that it is bounded below by a known constant. The loss function is scale invariant squared error. A class of minimax estimators is presented when the scale parameter of the distribution is known. In consequence, it has been shown that the generalized Bayes estimator with respect to the uniform prior on the truncated parameter space dominates the minimum risk equivariant estimator. By making use of a sequence of proper priors, we also show that this estimator is admissible for estimating the lower bounded shape parameter. A class of truncated linear estimators is studied as well. Some complete class results and a class of minimax estimators for the case of an unknown scale parameter are obtained. The corresponding generalized Bayes estimator is shown to be minimax in this case as well. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Restricted maximum likelihood estimator; Generalized Bayes estimator; Integral expression of risk difference; Scale invariance; Stein-type estimator; 62F10; 62C15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:79:y:2016:i:1:p:91-111

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DOI: 10.1007/s00184-015-0545-9

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