A Cramer-Rao analogue for median-unbiased estimators.

Sung, 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 -