# A Cramer-Rao analogue for median-unbiased estimators.

N. K. Sung; Gabriela Stangenhaus; Herbert T. David

Trabajos de Estadística (1990)

- Volume: 5, Issue: 2, page 83-94
- ISSN: 0213-8190

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topSung, N. K., Stangenhaus, Gabriela, and David, Herbert T.. "A Cramer-Rao analogue for median-unbiased estimators.." Trabajos de Estadística 5.2 (1990): 83-94. <http://eudml.org/doc/40563>.

@article{Sung1990,

abstract = {Adopting a measure of dispersion proposed by Alamo [1964], and extending the analysis in Stangenhaus [1977] and Stangenhaus and David [1978b], an analogue of the classical Cramér-Rao lower bound for median-unbiased estimators is developed for absolutely continuous distributions with a single parameter, in which mean-unbiasedness, the Fisher information, and the variance are replaced by median-unbiasedness, the first absolute moment of the sample score, and the reciprocal of twice the median-unbiased estimator's density height evaluated at its median point. We exhibit location-parameter and scale-parameter families for which there exist median-unbiased estimators meeting the bound. We also give an analogue of the Chapman-Robbins inequality which is free from regularity conditions.},

author = {Sung, N. K., Stangenhaus, Gabriela, David, Herbert T.},

journal = {Trabajos de Estadística},

keywords = {Estimadores insesgados; Dispersiones; Mediana; diffusivity; Cramér-Rao lower bound; median-unbiased estimators; absolutely continuous distributions; mean-unbiasedness; Fisher information; location-parameter; scale-parameter families; Chapman- Robbins inequality},

language = {eng},

number = {2},

pages = {83-94},

title = {A Cramer-Rao analogue for median-unbiased estimators.},

url = {http://eudml.org/doc/40563},

volume = {5},

year = {1990},

}

TY - JOUR

AU - Sung, N. K.

AU - Stangenhaus, Gabriela

AU - David, Herbert T.

TI - A Cramer-Rao analogue for median-unbiased estimators.

JO - Trabajos de Estadística

PY - 1990

VL - 5

IS - 2

SP - 83

EP - 94

AB - Adopting a measure of dispersion proposed by Alamo [1964], and extending the analysis in Stangenhaus [1977] and Stangenhaus and David [1978b], an analogue of the classical Cramér-Rao lower bound for median-unbiased estimators is developed for absolutely continuous distributions with a single parameter, in which mean-unbiasedness, the Fisher information, and the variance are replaced by median-unbiasedness, the first absolute moment of the sample score, and the reciprocal of twice the median-unbiased estimator's density height evaluated at its median point. We exhibit location-parameter and scale-parameter families for which there exist median-unbiased estimators meeting the bound. We also give an analogue of the Chapman-Robbins inequality which is free from regularity conditions.

LA - eng

KW - Estimadores insesgados; Dispersiones; Mediana; diffusivity; Cramér-Rao lower bound; median-unbiased estimators; absolutely continuous distributions; mean-unbiasedness; Fisher information; location-parameter; scale-parameter families; Chapman- Robbins inequality

UR - http://eudml.org/doc/40563

ER -

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