Minimum disparity estimators for discrete and continuous models

María Luisa Menéndez; Domingo Morales; Leandro Pardo; Igor Vajda

Applications of Mathematics (2001)

  • Volume: 46, Issue: 6, page 439-466
  • ISSN: 0862-7940

Abstract

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Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.

How to cite

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Menéndez, María Luisa, et al. "Minimum disparity estimators for discrete and continuous models." Applications of Mathematics 46.6 (2001): 439-466. <http://eudml.org/doc/33096>.

@article{Menéndez2001,
abstract = {Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.},
author = {Menéndez, María Luisa, Morales, Domingo, Pardo, Leandro, Vajda, Igor},
journal = {Applications of Mathematics},
keywords = {divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency; divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency},
language = {eng},
number = {6},
pages = {439-466},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Minimum disparity estimators for discrete and continuous models},
url = {http://eudml.org/doc/33096},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Menéndez, María Luisa
AU - Morales, Domingo
AU - Pardo, Leandro
AU - Vajda, Igor
TI - Minimum disparity estimators for discrete and continuous models
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 6
SP - 439
EP - 466
AB - Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.
LA - eng
KW - divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency; divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency
UR - http://eudml.org/doc/33096
ER -

References

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