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.
@article{urn:eudml:doc:40563,
title = {A Cramer-Rao analogue for median-unbiased estimators.},
journal = {Trabajos de Estad\'\i stica},
volume = {5},
year = {1990},
pages = {83-94},
zbl = {0743.62022},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40563}
}
Sung, N. K.; Stangenhaus, Gabriela; David, Herbert T. A Cramer-Rao analogue for median-unbiased estimators.. Trabajos de Estadística, Tome 5 (1990) pp. 83-94. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40563/