An admissible estimator of a lower-bounded scale parameter under squared-log error loss function

Eisa Mahmoudi; Hojatollah Zakerzadeh

Kybernetika (2011)

  • Volume: 47, Issue: 4, page 595-611
  • ISSN: 0023-5954

Abstract

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Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.

How to cite

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Mahmoudi, Eisa, and Zakerzadeh, Hojatollah. "An admissible estimator of a lower-bounded scale parameter under squared-log error loss function." Kybernetika 47.4 (2011): 595-611. <http://eudml.org/doc/196491>.

@article{Mahmoudi2011,
abstract = {Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.},
author = {Mahmoudi, Eisa, Zakerzadeh, Hojatollah},
journal = {Kybernetika},
keywords = {admissibility; Bayes estimator; truncated parameter spaces; squared-log error loss; Bayes estimator; truncated parameter spaces},
language = {eng},
number = {4},
pages = {595-611},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An admissible estimator of a lower-bounded scale parameter under squared-log error loss function},
url = {http://eudml.org/doc/196491},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Mahmoudi, Eisa
AU - Zakerzadeh, Hojatollah
TI - An admissible estimator of a lower-bounded scale parameter under squared-log error loss function
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 4
SP - 595
EP - 611
AB - Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.
LA - eng
KW - admissibility; Bayes estimator; truncated parameter spaces; squared-log error loss; Bayes estimator; truncated parameter spaces
UR - http://eudml.org/doc/196491
ER -

References

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