A Cramer-Rao analogue for median-unbiased estimators
- Autores: N. K. Sung, Gabriela Stangenhaus, Herbert T. David
- Localización: Trabajos de estadística, ISSN 0213-8190, Vol. 5, Nº. 2, 1990, págs. 83-94
- Idioma: inglés
- DOI: 10.1007/bf02863649
- Títulos paralelos:
- Análogo de la cota de Cramer-Rao para estimadores insesgados en la mediana
- Enlaces
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Resumen
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
