The lower bound for the variance of unbiased estimators for one-directional family of distributions

  • Masafumi Akahira
  • Kei Takeuchi


In this paper we introduce the concept of one-directionality which includes both cases of location (and scale) parameter and selection parameter and also other cases, and establish some theorems for shapr lower bounds and for the existence of zero variance unbiased estimator for this class of non-regular distributions.

Key words and phrases

Cramér-Rao bound Bhattacharyya bound unbiased estimator one-directional family of distributions sharp lower bound 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1987

Authors and Affiliations

  • Masafumi Akahira
    • 1
    • 2
  • Kei Takeuchi
    • 1
    • 2
  1. 1.University of Electro-CommunicationsTokyo
  2. 2.University of TokyoTokyoJapan

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