( h , Φ ) -entropy differential metric

María Luisa Menéndez; Domingo Morales; Leandro Pardo; Miquel Salicrú

Applications of Mathematics (1997)

  • Volume: 42, Issue: 2, page 81-98
  • ISSN: 0862-7940

Abstract

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Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on ( h , Φ ) -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic distances in testing statistical hypotheses is illustrated by an example within the Pareto family. We obtain the asymptotic distribution of the information matrices associated with the metric when the parameter is replaced by its maximum likelihood estimator. The relation between the information matrices and the Cramér-Rao inequality is also obtained.

How to cite

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Menéndez, María Luisa, et al. "$(h,\Phi )$-entropy differential metric." Applications of Mathematics 42.2 (1997): 81-98. <http://eudml.org/doc/32970>.

@article{Menéndez1997,
abstract = {Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on $(h,\Phi )$-entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic distances in testing statistical hypotheses is illustrated by an example within the Pareto family. We obtain the asymptotic distribution of the information matrices associated with the metric when the parameter is replaced by its maximum likelihood estimator. The relation between the information matrices and the Cramér-Rao inequality is also obtained.},
author = {Menéndez, María Luisa, Morales, Domingo, Pardo, Leandro, Salicrú, Miquel},
journal = {Applications of Mathematics},
keywords = {$(h,\Phi )$-entropy measures; information metric; geodesic distance between probability distributions; maximum likelihood estimators; asymptotic distributions; Cramér-Rao inequality.; generalized entropies; information metric; generalized entropies; geodesic distance},
language = {eng},
number = {2},
pages = {81-98},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$(h,\Phi )$-entropy differential metric},
url = {http://eudml.org/doc/32970},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Menéndez, María Luisa
AU - Morales, Domingo
AU - Pardo, Leandro
AU - Salicrú, Miquel
TI - $(h,\Phi )$-entropy differential metric
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 2
SP - 81
EP - 98
AB - Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on $(h,\Phi )$-entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic distances in testing statistical hypotheses is illustrated by an example within the Pareto family. We obtain the asymptotic distribution of the information matrices associated with the metric when the parameter is replaced by its maximum likelihood estimator. The relation between the information matrices and the Cramér-Rao inequality is also obtained.
LA - eng
KW - $(h,\Phi )$-entropy measures; information metric; geodesic distance between probability distributions; maximum likelihood estimators; asymptotic distributions; Cramér-Rao inequality.; generalized entropies; information metric; generalized entropies; geodesic distance
UR - http://eudml.org/doc/32970
ER -

References

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