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Inadmissible estimators of normal quantiles and two-sample problems with additional information

Éric Marchand, Mohammad Jafari Jozani, and Yogesh Mani Tripathi

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Abstract

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.

Chapter information

Source
Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 104-116

Dates
First available in Project Euclid: 14 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1331731615

Digital Object Identifier
doi:10.1214/11-IMSCOLL808

Zentralblatt MATH identifier
1326.62055

Subjects
Primary: 62F10: Point estimation 62F30: Inference under constraints 62C15: Admissibility

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

Citation

Marchand, Éric; Jafari Jozani, Mohammad; Mani Tripathi, Yogesh. Inadmissible estimators of normal quantiles and two-sample problems with additional information. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 104--116, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL808. https://projecteuclid.org/euclid.imsc/1331731615


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