Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Chapman-Robbins-type and Bayesian lower bounds based on diffusivity for median-unbiased estimators

  • Kyung, Sung-Nae (Statistics Department, Ewha Womans University, Seoul 120-750)
  • Published : 1997.12.01
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Abstract

A more generalized version of the information inequality based on diffusivity which is a natural measure of dispersion for median-unbiased estimators developed by Sung et al. (1990) is presented. This non-Bayesian L$_{1}$ information inequality is free from regularity conditions and can be regarded as an analogue of the Chapman-Robbins inequality for mean-unbiased estimation. The approach given here, however, deals with a more generalized situation than that of the Chapman-Robbins inequality. We also develop a Bayesian version of the L$_{1}$ information inequality in median-unbiased estimation. This latter inequality is directly comparable to the Bayesian Cramer-Rao bound due to the van Trees inequality.

Keywords

References

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