Open Access
VOL. 8 | 2012 Inadmissible estimators of normal quantiles and two-sample problems with additional information
Éric Marchand, Mohammad Jafari Jozani, Yogesh Mani Tripathi

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 104-116 (2012) DOI: 10.1214/11-IMSCOLL808


We consider estimation problem of a normal quantile μ+ησ. For the scale invariant squared error loss and unrestricted values of the population mean and standard deviation μ and σ, [13] established the inadmissibility of the MRE estimator for η0. In this paper, we explore: (i) the impact of the loss with the study of scale invariant absolute value loss, and (ii) situations where there is a parameter space restriction of a lower bounded mean μ. We establish

(i) the inadmissibility of the MRE estimator of μ+ησ; η0; under scale invariant absolute value loss;

(ii) the inadmissibility of the Generalized Bayes estimator of μ+ησ; η>0; under scale invariant squared error loss, associated with the prior measure 1(0,)(μ)1(0,)(σ) which represents the truncation of the usual non-informative prior measure onto the restricted parameter space.

Both of these results are obtained through a conditional risk analysis and may be viewed as extensions of [13]. Finally, we provide further applications to two-sample problems under the presence of the additional information of ordered means.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1326.62055
MathSciNet: MR3202506

Digital Object Identifier: 10.1214/11-IMSCOLL808

Primary: 62C15 , 62F10 , 62F30

Keywords: absolute value loss , Additional information , complete class , conditional risk , estimation , inadmissibility , normal quantiles , restricted parameter space , squared error loss

Rights: Copyright © 2012, Institute of Mathematical Statistics

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