On estimation and adaptive estimation for locally asymptotically normal families

  • Václav Fabian
  • James Hannan


Locally asymptotically minimax (LAM) estimates are constructed for locally asymptotically normal (LAN) families under very mild additional assumptions. Adaptive estimation is also considered and a sufficient condition is given for an estimate to be locally asymptotically minimax adaptive. Incidently, it is shown that a well known lower bound due to Hájek (1972) for the local asymptotic minimax risk is not sharp.


Stochastic Process Probability Theory Mathematical Biology Additional Assumption Normal Family 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Václav Fabian
    • 1
    • 2
  • James Hannan
    • 2
  1. 1.University of BernSwitzerland
  2. 2.Dept. of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

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