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A cramer-Rao analogue for median-unbiased estimators
- A cramer-Rao analogue for median-unbiased estimators
- Sung N.K.; Stangenhaus G.; David H.T.
- Ewha Authors
- Issue Date
- Journal Title
- Trabajos de Estadistica
- vol. 5, no. 2, pp. 83 - 94
- Adopting a measure of dispersion proposed by Alamo , and extending the analysis in Stangenhaus  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. © 1990 Springer.
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