DOI QR코드

DOI QR Code

A Bhattacharyya Analogue for Median-unbiased Estimation

  • Published : 2004.04.01

Abstract

A more general version of diffusivity based on total variation of density is defined and an information inequality for median-unbiased estimation is presented. The resulting information inequality can be interpreted as an analogue of the Bhattacharyya system of lower bounds for mean-unbiased estimation. A condition on which the information bound is achieved is also given.

References

  1. Sankhya v.8 On Some analogues to the amount of information and their uses in statistical estimation Bhattacharyya,A.
  2. Contributions to Statistics: Jaroslav Hajek memorial volume Descriptive Statistics for Nonparametric Models Ⅳ. Spread Bickel,P.J.;Lehmann,E.L.
  3. Annals of Mathematical Statistics v.32 A unified theory of estimators Ⅰ Birnbaum,A. https://doi.org/10.1214/aoms/1177705145
  4. Annals of Mathematical Statistics v.30 On the attainment of Cramer-Rao and Bhattacharyya bounds for the variances of an estimate Fend,A.V. https://doi.org/10.1214/aoms/1177706258
  5. Trabajos de Estadistica v.5 A Cramer-Rao analogue for median-unbiased estimators Sung,N.K.;Stangenhaus,G.;David,H.T. https://doi.org/10.1007/BF02863649
  6. Journal of Multivariate Analysis v.32 A generalized Cramer-Rao analogue for median-unbiased estimators Sung,N.K. https://doi.org/10.1016/0047-259X(90)90081-R
  7. Journal of the Korean Statistical Society v.19 An optimality criterion for median-unbiased estimators Sung,N.K.
  8. Journal of the Korean Statistical Society v.22 no.1 Improving L₁information bound for median-unbiased estimators in the presence of a nuisance parameter Sung,N.K.
  9. Journal of the Korean Statistical Society v.26 no.4 Chapman-Robbins-type and Bayesian lower bound based on diffusivity Sung,N.K.