Several applications of divergence criteria in continuous families

Michel Broniatowski; Igor Vajda

Kybernetika (2012)

  • Volume: 48, Issue: 4, page 600-636
  • ISSN: 0023-5954

Abstract

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This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese and Vajda [9] and independently Broniatowski and Keziou [3], called here power superdivergence estimators, (ii) by Broniatowski and Keziou [4], called here power subdivergence estimators, (iii) by Basu et al. [2], called here power pseudodistance estimators, and (iv) by Vajda [18] called here Rényi pseudodistance estimators. These various criterions have in common to eliminate all need for grouping or smoothing in statistical inference. The paper studies and compares general properties of these estimators such as Fisher consistency and influence curves, and illustrates these properties by detailed analysis of the applications to the estimation of normal location and scale.

How to cite

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Broniatowski, Michel, and Vajda, Igor. "Several applications of divergence criteria in continuous families." Kybernetika 48.4 (2012): 600-636. <http://eudml.org/doc/246232>.

@article{Broniatowski2012,
abstract = {This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese and Vajda [9] and independently Broniatowski and Keziou [3], called here power superdivergence estimators, (ii) by Broniatowski and Keziou [4], called here power subdivergence estimators, (iii) by Basu et al. [2], called here power pseudodistance estimators, and (iv) by Vajda [18] called here Rényi pseudodistance estimators. These various criterions have in common to eliminate all need for grouping or smoothing in statistical inference. The paper studies and compares general properties of these estimators such as Fisher consistency and influence curves, and illustrates these properties by detailed analysis of the applications to the estimation of normal location and scale.},
author = {Broniatowski, Michel, Vajda, Igor},
journal = {Kybernetika},
keywords = {divergence; parametric estimation; robustness; robustness; divergence; parametric estimation},
language = {eng},
number = {4},
pages = {600-636},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Several applications of divergence criteria in continuous families},
url = {http://eudml.org/doc/246232},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Broniatowski, Michel
AU - Vajda, Igor
TI - Several applications of divergence criteria in continuous families
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 4
SP - 600
EP - 636
AB - This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese and Vajda [9] and independently Broniatowski and Keziou [3], called here power superdivergence estimators, (ii) by Broniatowski and Keziou [4], called here power subdivergence estimators, (iii) by Basu et al. [2], called here power pseudodistance estimators, and (iv) by Vajda [18] called here Rényi pseudodistance estimators. These various criterions have in common to eliminate all need for grouping or smoothing in statistical inference. The paper studies and compares general properties of these estimators such as Fisher consistency and influence curves, and illustrates these properties by detailed analysis of the applications to the estimation of normal location and scale.
LA - eng
KW - divergence; parametric estimation; robustness; robustness; divergence; parametric estimation
UR - http://eudml.org/doc/246232
ER -

References

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